The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment.

vi, 161 p Bibliography: p. 157-158

By J. H. Wilkinson, C. Reinsch ; Edited By F. L. Bauer.

By J. H. Wilkinson, C. Reinsch ; Edited By F. L. Bauer.

This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. It also lays the foundation for the language and framework for modern analysis and its applications. Divided into seven chapters, it discusses vector spaces, linear transformations, best approximation in inner product spaces, eigenvalues and eigenvectors, block diagonalisation, triangularisation, Jordan form, singular value decomposition, polar decomposition, and many more topics that are relevant to applications. The topics chosen have become well-established over the years and are still very much in use. The approach is both geometric and algebraic. It avoids distraction from the main theme by deferring the exercises to the end of each section. These exercises aim at reinforcing the learned concepts rather than as exposing readers to the tricks involved in the computation. Problems included at the end of each chapter are relatively advanced and require a deep understanding and assimilation of the topics.-- Provided by publisher

<p>This volume, which became a classic on first publication, is perhaps the most important and widely read book in the field of numerical analysis. It presents a distillation of the author's pioneering discoveries concerning the computation of matrix eigenvalues. The emphasis is on the transmission of knowledge rather than elaborate proofs. The book will be valued by all practicing numerical analysts, students and researchers in the field, engineers, and scientists.</p> <p>The book will be valued by all practicing numerical analysts, students and researchers in the field, engineers, and scientists. </p>

xviii, 662 p. 25 cm Bibliography: p. [649]-655

The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment. Erscheinungsdatum: 23.08.2014

The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment.

The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment.

225 pages ; 18 cm

<p>Published to honor the late Jim Wilkinson, the respected pioneer in numerical analysis, this book includes contributions from his colleagues and collaborators, leading experts in their own right. The breadth of Wilkinson's research is reflected in the topics covered, which include linear algebra, error analysis and computer arithmetic algorithms, and mathematical software. An invaluable reference, the book is completely up-to-date with the latest developments on the Lanczos algorithm, QR-factorizations, error propagation models, parameter estimation problems, sparse systems, and shape-preserving splines. Reflecting the current growth and vitality of this field, the volume is an essential reference for all numerical analysts.</p>

This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. It also lays the foundation for the language and framework for modern analysis and its applications. Divided into seven chapters, it discusses vector spaces, linear transformations, best approximation in inner product spaces, eigenvalues and eigenvectors, block diagonalisation, triangularisation, Jordan form, singular value decomposition, polar decomposition, and many more topics that are relevant to applications. The topics chosen have become well-established over the years and are still very much in use. The approach is both geometric and algebraic. It avoids distraction from the main theme by deferring the exercises to the end of each section. These exercises aim at reinforcing the learned concepts rather than as exposing readers to the tricks involved in the computation. Problems included at the end of each chapter are relatively advanced and require a deep understanding and assimilation of the topics.-- Provided by publisher

This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. It also lays the foundation for the language and framework for modern analysis and its applications. Divided into seven chapters, it discusses vector spaces, linear transformations, best approximation in inner product spaces, eigenvalues and eigenvectors, block diagonalisation, triangularisation, Jordan form, singular value decomposition, polar decomposition, and many more topics that are relevant to applications. The topics chosen have become well-established over the years and are still very much in use. The approach is both geometric and algebraic. It avoids distraction from the main theme by deferring the exercises to the end of each section. These exercises aim at reinforcing the learned concepts rather than as exposing readers to the tricks involved in the computation. Problems included at the end of each chapter are relatively advanced and require a deep understanding and assimilation of the topics.-- Provided by publisher

<p>This volume, which became a classic on first publication, is perhaps the most important and widely read book in the field of numerical analysis. It presents a distillation of the author's pioneering discoveries concerning the computation of matrix eigenvalues. The emphasis is on the transmission of knowledge rather than elaborate proofs. The book will be valued by all practicing numerical analysts, students and researchers in the field, engineers, and scientists.</p> <p>The book will be valued by all practicing numerical analysts, students and researchers in the field, engineers, and scientists. </p>

This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. It also lays the foundation for the language and framework for modern analysis and its applications. Divided into seven chapters, it discusses vector spaces, linear transformations, best approximation in inner product spaces, eigenvalues and eigenvectors, block diagonalisation, triangularisation, Jordan form, singular value decomposition, polar decomposition, and many more topics that are relevant to applications. The topics chosen have become well-established over the years and are still very much in use. The approach is both geometric and algebraic. It avoids distraction from the main theme by deferring the exercises to the end of each section. These exercises aim at reinforcing the learned concepts rather than as exposing readers to the tricks involved in the computation. Problems included at the end of each chapter are relatively advanced and require a deep understanding and assimilation of the topics.-- Provided by publisher

Heidelberger Taschenbücher Erscheinungsdatum: 01.01.1969

1 (p1): 第一章 理论基础 1 (p1-2): 引言 2 (p1-3): 定义 3 (p1-4): 转置矩阵的特征值与特征向量 4 (p1-5): 不相同的特征值 6 (p1-6): 相似变换 7 (p1-7): 重特征值与一般矩阵的标准型 8 (p1-8): 亏损特征向量系 10 (p1-9): Jordan(经典的)标准型 11 (p1-10): 初等因子 12 (p1-11): A的特征多项式的友矩阵 13 (p1-12): 非减次矩阵 15 (p1-13): Frobenius(有理的)标准型 16 (p1-14): Jordan标准型与Frobenius标准型的关系 17 (p1-15): 相抵变换 18 (p1-16): λ矩阵 19 (p1-17): 初等运算 19 (p1-18): Smith标准型 22 (p1-19): λ矩阵的κ行子式的最大公因子 22 (p1-20): (A-λI)的不变因子 24 (p1-21): 三角标准型 24 (p1-22): Hermite矩阵与对称矩阵 25 (p1-23): Hermite矩阵的基本性质 27 (p1-24): 复对称矩阵 27 (p1-25): 用酉变换化成三角型 27 (p1-26): 二次型 29 (p1-27): 正定性的充要条件 30 (p1-28): 常系数微分方程 31 (p1-29): 对应于非线性初等因子的解 33 (p1-30): 高阶微分方程 34 (p1-31): 特殊形式的二阶方程 35 (p1-32): By--Ay的显式解 36 (p1-33): 形如(AB-λI)x=0的方程 37 (p1-34): 向量的最小多项式 38 (p1-35): 矩阵的最小多项式 39 (p1-36): Cayley-Hamilton定理 40 (p1-37): 最小多项式与标准型的关系 43 (p1-38): 主向量 44 (p1-39): 初等相似变换 46 (p1-40): 初等矩阵的性质 46 (p1-41): 用初等相似变换化成三角标准型 48 (p1-42): 初等酉变换 49 (p1-43): 初等酉Hermite矩阵 51 (p1-44): 用初等酉变换化成三角型 52 (p1-45): 正规矩阵 53 (p1-46): 可交换矩阵 55 (p1-47): AB的特征值 56 (p1-48): 向量与矩阵的范数 57 (p1-49): 从属的矩阵范数 58 (p1-50): Euclid范数与谱范数 59 (p1-51): 范数与极限 62 (p1-52): 避免使用矩阵无穷级数 64 (p2): 第二章 摄动理论 64 (p2-2): 引言 65 (p2-3): 关于特征值连续性的Ostrowski定理 66 (p2-4): 代数函数 67 (p2-5): 数值例题 68 (p2-6): 单特征值的摄动理论 69 (p2-7): 对应特征向量的摄动 70 (p2-8): 具有线性初等因子的矩阵 71 (p2-9): 特征值的一阶摄动 72 (p2-10): 高阶摄动 72 (p2-11): 特征向量的一阶摄动 73 (p2-12): 重特征值 73 (p2-13): Gerschgorin定理 75 (p2-14): 基于Gerschgorin定理的摄动理论 75 (p2-15): 情形1 具有线性初等因子矩阵的单特征值λ1的摄动 78 (p2-16): 情形2 具有线性初等因子矩阵的重特征值λ1的摄动 80 (p2-17): 情形3 具有一个或多个非线性初等因子矩阵的单特征值的摄动 82 (p2-18): 情形4 相应于非减次矩阵非线性因子的特征值的摄动 83 (p2-19): 情形5 当有一个以上(λ？-λ)幂次的初等因子且至少有一个为非线性时，特征值λ？的摄动 84 (p2-20): 相应于非线性因子一般分布的摄动 84 (p2-21): 根据Jordan标准型的特征向量的摄动理论 86 (p2-22): 相应于重特征值(线性初等因子)的特征向量的摄动 87 (p2-23): 摄动理论的限度 88 (p2-24): si之间的关系 89 (p2-25): 条件数 89 (p2-26): 计算问题的条件 90 (p2-27): 矩阵A关于特征值问题的谱条件数 91 (p2-28): 谱条件数的性质 92 (p2-29): 条件数的不变性 93 (p2-30): 非常病态的矩阵 96 (p2-31): 实对称矩阵的摄动理论 96 (p2-32): 非对称摄动 97 (p2-33): 对称摄动 98 (p2-34): 经典方法 101 (p2-35): 秩为1的对称矩阵 102 (p2-36): 特征值的极值性质 103 (p2-37): 特征值的极小-极大性质 105 (p2-38): 两个对称矩阵之和的特征值 106 (p2-39): 实际应用 107 (p2-40): 分隔定理 107 (p2-41): 极小-极大原理的进一步应用 108 (p2-42): Wielandt-Hoffman定理 114 (p3): 第三章 误差分析 114 (p3-2): 引言 114 (p3-3): 定点运算 115 (p3-4): 内积的累加 116 (p3-5): 浮点运算 117 (p3-6): 误差界的简化表示 118 (p3-7): 某些基本浮点计算的误差界 119 (p3-8): 误差矩阵的范数的界 120 (p3-9): 浮点运算中内积的累加 121 (p3-10): 某些基本f？2()计算的误差界 123 (p3-11): 平方根的计算 123 (p3-12): 块浮点向量和矩阵 124 (p3-13): t位计算的基本限制 127 (p3-14): 用相似变换作简化的特征值方法 128 (p3-15): 基于初等非酉变换方法的误差分析 130 (p3-16): 基于初等酉变换的方法的误差分析 132 (p3-17): 酉变换的优越性 133 (p3-18): 实对称矩阵 134 (p3-19): 酉变换的限度 135 (p3-20): 用浮点计算的平面旋转的误差分析 137 (p3-21): 用平面旋转的乘法 139 (p3-22): 用一系列平面旋转做乘法 144 (p3-23): 近似的平面旋转乘积的误差 145 (p3-24): 相似变换的误差 146 (p3-25): 对称矩阵 148 (p3-26): 定点运算的平面旋转 149 (p3-27): sinθ和cosθ的另一种算法 150 (p3-28): 用近似的定点旋转左乘 151 (p3-29): 用一系列平面旋转相乘(定点) 153 (p3-30): 一组近似平面旋转的计算乘积 153 (p3-31): 相似变换的误差 156 (p3-32): 关于误差界的总评述 157 (p3-33): 浮点计算的初等Hermite矩阵 158 (p3-34): 初等Hermite矩阵计算的误差分析 162 (p3-35): 数值例子 163 (p3-36): 用近似的初等Hermite矩阵左乘 166 (p3-37): 用近似的初等Hermite矩阵序列的乘法 168 (p3-38): 类似平面旋转的非酉初等矩阵 169 (p3-39): 类似于初等Hermite矩阵的非酉初等矩阵 171 (p3-40): 用非酉矩阵序列左乘 172 (p3-41): 先验的误差界 173 (p3-42): 正规性的偏离 175 (p3-43): 简单的例子 176 (p3-44): 后验的界 177 (p3-45): 正规矩阵的后验的界 178 (p3-46): Rayleigh商 180 (p3-47): Rayleigh商的误差 181 (p3-48): Hermite矩阵 183 (p3-49): 病态地靠近的特征值 185 (p3-50): 非正规矩阵 187 (p3-51): 完全特征系的误差分析 188 (p3-52): 数值例子 189 (p3-53): 限制可达精度的条件 190 (p3-54): 非线性初等因子 192 (p3-55): 近似的不变子空间 195 (p3-56): 几乎正规矩阵 197 (p4): 第四章 线性代数方程组的解法 197 (p4-2): 引言 197 (p4-3): 摄动理论 199 (p4-4): 条件数 200 (p4-5): 平衡矩阵 201 (p4-6): 简单的实际例子 201 (p4-7): 特征向量矩阵的条件 202 (p4-8): 显式解 203 (p4-9): 对矩阵条件的总评述 204 (p4-10): 病态和几乎奇异的关系 205 (p4-11): t位运算的限制 206 (p4-12): 解线性方程组的算法 208 (p4-13): Gauss消去法 208 (p4-14): 三角形分解 209 (p4-15): 三角形分解矩阵的结构 210 (p4-16): 三角形矩阵元素的显式表达式 212 (p4-17): Gauss消去法的中断 213 (p4-18): 数值稳定性 214 (p4-19): 交换的重要性 215 (p4-20): 数值例子 217 (p4-21): Gauss消去法的误差分析 219 (p4-22): 用定点运算的摄动矩阵的上界 220 (p4-23): 约化后的矩阵元素的上界 220 (p4-24): 全主元素 222 (p4-25): 部分主元素方法的实际过程 222 (p4-26): 浮点误差分析 224 (p4-27): 不选主元素的浮点分解 225 (p4-28): 有效位的损失 225 (p4-29): 流传的谬误 226 (p4-30): 特殊形式的矩阵 229 (p4-31): 在高速计算机上的Gauss消去法 230 (p4-32): 对应不同的右端的解 230 (p4-33): 直接的三角形分解 231 (p4-34): Gauss消去法和直接的三角形分解的关系 232 (p4-35): 分解不唯一和失败的例子 233 (p4-36): 有行交换的三角形分解 236 (p4-37): 三角形分解的误差分析 238 (p4-38): 行列式计算 238 (p4-39): Cholesky分解 239 (p4-40): 对称非正定矩阵 240 (p4-41): 定点运算Cholesky分解的误差分析 242 (p4-42): 病态矩阵 243 (p4-43): 用初等Hermite矩阵的三角形化 246 (p4-44): Householder三角形化的误差分析 246 (p4-45): 用M′ii型初等稳定矩阵的三角形化 247 (p4-46): 前主子式的计算 249 (p4-47): 用平面旋转的三角形化 250 (p4-48): Givens约化的误差分析 251 (p4-49): 正交三角形化的唯一性 252 (p4-50): Schmidt正交化 254 (p4-51): 三角形化方法的比较 256 (p4-52): 向后回代 259 (p4-53): 三角形方程组的计算解的高精度 261 (p4-54): 一般的方程组的解 262 (p4-55): 一般矩阵的逆的计算 263 (p4-56): 计算解的精度 264 (p4-57): 没有小主元素的病态矩阵 265 (p4-58): 近似解的迭代改进 266 (p4-59): 迭代过程中舍入误差的影响 267 (p4-60): 定点计算的迭代过程 268 (p4-61): 迭代过程的一个简单例子 270 (p4-62): 迭代过程的总评述 271 (p4-63): 有关的迭代法 272 (p4-64): 迭代过程的极限 272 (p4-65): 迭代法的严格的调整 275 (p4-66): 实对称矩阵的经典Jacobi方法 275 (p5): 第五章 Hermite矩阵 275 (p5-2): 引言 277 (p5-3): 收敛率 278 (p5-4): 收敛于固定的对角矩阵 279 (p5-5): 顺序Jacobi方法 280 (p5-6): Gerschgorin圆 280 (p5-7): Jacobi方法的最后的二次收敛性 282 (p5-8): 靠近的和重的特征值 283 (p5-9): 数值例子 284 (p5-10): cosθ与sinθ的计算 287 (p5-11): 更简单的转角计算方法 288 (p5-12): 过关Jacobi方法 289 (p5-13): 特征向量计算 289 (p5-14): 数值例子 290 (p5-15): Jacobi方法的舍入误差 291 (p5-16): 计算的特征向量的精确度 292 (p5-17): 用定点计算的误差界 293 (p5-18): 程序编制问题 293 (p5-19): Givens方法 295 (p5-20): 在有两级存储设备的计算机上实现Givens方法 297 (p5-21): Givens方法的浮点误差分析 298 (p5-22): 定点误差分析 299 (p5-23): 数值例子 302 (p5-24): Householder方法 304 (p5-25): 利用对称性 304 (p5-26): 存储方案的研究 305 (p5-27): 在有内、外存储设备的计算机上实现Householder方法 306 (p5-28): 用定点运算的Householder方法 307 (p5-29): 数值例子 309 (p5-30): Householder方法的误差分析 310 (p5-31): 对称三对角矩阵的特征值 311 (p5-32): Sturm序列性质 313 (p5-33): 分半法 314 (p5-34): 分半法的数值稳定性 317 (p5-35): 数值例子 318 (p5-36): 关于分半法的总评述 319 (p5-37): 小特征值 319 (p5-38): 靠近的特征值和小β？ 324 (p5-39): 特征值的定点计算 327 (p5-40): 三对角型的特征向量计算 328 (p5-41): 特征向量显式表达式的不稳定性 330 (p5-42): 数值例子 333 (p5-43): 逆迭代 335 (p5-44): 初始向量b的选择 336 (p5-45): 误差分析 337 (p5-46): 数值例子 339 (p5-47): 靠近的特征值和小的β？ 340 (p5-48): 对应重特征值的线性独立特征向量 343 (p5-49): 计算特征向量的交替方法 344 (p5-50): 数值例子 344 (p5-51): 三对角矩阵特征问题的评论 345 (p5-52): Givens和Householder方法的完成 347 (p5-53): 方法的比较 348 (p5-54): 拟对称三对角矩阵 349 (p5-55): 特征向量的计算 349 (p5-56): 形如Ax=λBx和ABx=λx的方程 351 (p5-57): 数值例子 352 (p5-58): 同时简化A和B为对角型 353 (p5-59): 三对角矩阵A和B 354 (p5-60): 复Hermite矩阵 359 (p5-61): Givens方法 359 (p6): 第六章 化一般矩阵为压缩型 359 (p6-2): 引言 361 (p6-3): Householder方法 364 (p6-4): 存储方案的研究 365 (p6-5): 误差分析 366 (p6-6): Givens方法与Householder方法的关系 368 (p6-7): 初等稳定变换 370 (p6-8): 置换的意义 371 (p6-9): 直接约化矩阵为Hessenberg型 373 (p6-10): 结合交换 374 (p6-11): 数值例子 378 (p6-12): 误差分析 380 (p6-13): 有关的误差分析 383 (p6-14): Hessenberg矩阵的劣定 383 (p6-15): 用M′？i型稳定矩阵化为Hessenberg型 384 (p6-16): Krylov方法 385 (p6-17): 逐列Gauss消去法 386 (p6-18): 实际的困难 387 (p6-19): 对于某些标准的特征值分布的C的条件 389 (p6-20): 级小于n的初始向量 391 (p6-21): 实际的经验 392 (p6-22): 广义Hessenberg方法 393 (p6-23): 广义Hessenberg方法的失败 395 (p6-24): Hessenberg方法 395 (p6-25): 实际的方法 396 (p6-26): Hessenberg方法与以前的方法的关系 397 (p6-27): Arnoldi方法 398 (p6-28): 实际的考虑 400 (p6-29): 再正交化的重要性 403 (p6-30): Lanczos方法 404 (p6-31): 过程的故障 406 (p6-32): 数值例子 406 (p6-33): 实际的Lanczos方法 408 (p6-34): 数值例子 409 (p6-35): 非对称的Lanczos方法的总评述 410 (p6-36): 对称的Lanczos方法 411 (p6-37): 化Hessenberg矩阵为更压缩的形式 411 (p6-38): 化下Hessnberg矩阵为三对角型 412 (p6-39): 使用交换 414 (p6-40): 小主元素的影响 415 (p6-41): 误差分析 417 (p6-42): 应用于下Hessenberg型的Hessenberg方法 418 (p6-43): Hessenberg方法与Lanczos方法的关系 419 (p6-44): 化一般矩阵为三对角型 420 (p6-45): 化矩阵为三对角型的重新考察 420 (p6-46): 和Lanczos方法比较 421 (p6-47): 化上Hessenberg型为Probenius型 423 (p6-48): 小主元素的影响 423 (p6-49): 数值例子 424 (p6-50): 关于稳定性的总评述 425 (p6-51): 特殊的上Hessenberg型 426 (p6-52): 直接确定特征多项式 429 (p7): 第七章 压缩型矩阵的特征值 429 (p7-2): 引言 429 (p7-3): 显式多项式形式 432 (p7-4): 显式多项式的条件数 433 (p7-5): 某些典型的零点分布 437 (p7-6): Krylov 方法的总评述 437 (p7-7): 显式多项式的总评述 439 (p7-8): 三对角矩阵 442 (p7-9): Hessenberg矩阵的行列式 443 (p7-10): 舍入误差的影响 445 (p7-11): 浮点累加 446 (p7-12): 用正交变换计算 448 (p7-13): 一般矩阵的行列式计算 448 (p7-14): 文义特征值问题 449 (p7-15): 间接确定特征多项式 450 (p7-16): Le Verrier方法 451 (p7-17): 以插值为基础的迭代法 452 (p7-18): 渐近收敛率 454 (p7-19): 多重零点 456 (p7-20): 函数关系的逆 458 (p7-21): 区间分半法 458 (p7-22): Newton法 459 (p7-23): Newton法与插值法的比较 460 (p7-24): 三次收敛的方法 461 (p7-25): Laguerre方法 464 (p7-26): 复零点 465 (p7-27): 复共轭零点 467 (p7-28): Bairstow方法 468 (p7-29): 广义的Bairstow方法 470 (p7-30): 实际的考虑 471 (p7-31): 舍入误差对渐近收敛性的影响 471 (p7-32): 区间分半法 473 (p7-33): 逐次线性插值 475 (p7-34): 多重的和病态靠近的特征值 476 (p7-35): 其他的插值法 478 (p7-36): 使用导数的方法 479 (p7-37): 接收零点的准则 480 (p7-38): 舍入误差的影响 481 (p7-39): 消除已计算的零点 482 (p7-40): Hessenberg矩阵的降阶 485 (p7-41): 三对角矩阵的降阶 487 (p7-42): 用旋转或稳定的初等变换降阶 489 (p7-43): 降阶的稳定性 491 (p7-44): 关于降阶的总评述 491 (p7-45): 消除已计算的零点 492 (p7-46): 消除已计算的二次因子 493 (p7-47): 关于消除零点方法的总评述 495 (p7-48): 渐近收敛率 495 (p7-49): 大范围的收敛性 498 (p7-50): 复零点 499 (p7-51): 建议 500 (p7-52): 复矩阵 500 (p7-53): 含有独立参数的矩阵 503 (p8): 第八章 LR和QR算法 503 (p8-2): 引言 504 (p8-3): 有复特征值的实矩阵 505 (p8-4): LR算法 507 (p8-5): As的收敛性证明 511 (p8-6): 正定Hermite矩阵 512 (p8-7): 复共轭特征值 516 (p8-8): 引进交换 517 (p8-9): 数值例子 518 (p8-10): 修改过程的收敛性 519 (p8-11): 初始矩阵的预先约化 520 (p8-12): 上Hessenberg型的不变性 522 (p8-13): 行和列同时运算 523 (p8-14): 收敛的加速 524 (p8-15): 结合原点的移动 525 (p8-16): 选择原点的移动 527 (p8-17): 矩阵降阶 528 (p8-18): 关于收敛性的实际经验 529 (p8-19): 改进的移动策略 530 (p8-20): 复共轭特征值 532 (p8-21): 修正的LR算法的缺点 533 (p8-22): QR算法 534 (p8-23): QR算法的收敛性 535 (p8-24): 收敛性的正式证明 537 (p8-25): 特征值的不同顺序 538 (p8-26): 等模的特征值 539 (p8-27): LR算法的另一个证明 541 (p8-28): QR算法的实际应用 542 (p8-29): 原点移动 543 (p8-30): As的分解 544 (p8-31): 数值例子 545 (p8-32): 实际的方法 546 (p8-33): 避免复共轭位移 550 (p8-34): 用初等Hermite变换的双步QR 551 (p8-35): 计算的细节 552 (p8-36): As的分解 554 (p8-37): LR的双位移技术 555 (p8-38): 对LR算法和QR算法的评述 557 (p8-39): 多重特征值 561 (p8-40): 降阶法的特殊用途 561 (p8-41): 对称矩阵 562 (p8-42): LR算法与QR算法的关系 564 (p8-43): Cholesky LR算法的收敛性 565 (p8-44): QR算法的三次收敛性 568 (p8-45): Cholesky LR中的原点位移 568 (p8-46): Cholesky分解失败 570 (p8-47): 三次收敛的LR方法 572 (p8-48): 带状矩阵 575 (p8-49): 带状矩阵的QR分解 579 (p8-50): 误差分析 580 (p8-51): 非对称带状矩阵 583 (p8-52): 在Q算法中同时分解和复合 585 (p8-53): 缩小带宽 588 (p9): 第九章 迭代法 588 (p9-2): 引言 588 (p9-3): 幂法 589 (p9-4): 单个向量的直接迭代 590 (p9-5): 原点移动 591 (p9-6): 舍入误差的影响 594 (p9-7): р的变化 595 (p9-8): р的特别选择 596 (p9-9): Aitken的加速方法 597 (p9-10): 复共轭特征值 599 (p9-11): 复特征向量的计算 600 (p9-12): 原点移动 601 (p9-13): 非线性初等因子 602 (p9-14): 同时决定几个特征值 603 (p9-15): 复矩阵 603 (p9-16): 收缩法 604 (p9-17): 用相似变换的收缩法 605 (p9-18): 用不变子空间的收缩法 606 (p9-19): 用稳定初等变换的收缩法 608 (p9-20): 用酉变换的收缩法 609 (p9-21): 数值稳定性 611 (p9-22): 数值例子 613 (p9-23): 酉变换的稳定性 614 (p9-24): 非相似变换的收缩法 617 (p9-25): 用不变子空间的一般约化 620 (p9-26): 实际应用 621 (p9-27): 梯级迭代 623 (p9-28): 复共轭特征值的精度确定 625 (p9-29): 十分靠近的特征值 625 (p9-30): 正交化方法 626 (p9-31): 正交化的梯级迭代 628 (p9-32): 双迭代 629 (p9-33): 数值例子 633 (p9-34): Richardson改进方法 634 (p9-35): 矩阵平方法 636 (p9-36): 数值稳定性 637 (p9-37): Chebyshev多项式的使用 638 (p9-38): 关于直接迭代的总评述 638 (p9-39): 逆迭代 639 (p9-40): 逆迭代的误差分析 641 (p9-41): 分析的总评述 642 (p9-42): 特征向量的进一步改进 645 (p9-43): 非线性初等因子 646 (p9-44): Hessenberg矩阵的逆迭代 647 (p9-45): 退化情况 648 (p9-46): 带形矩阵逆迭代 649 (p9-47): 复共轭特征向量 651 (p9-48): 误差分析 652 (p9-49): 数值例子 654 (p9-50): 广义特征值问题 655 (p9-51): 近似特征值的变更 657 (p9-52): 特征系的改进 661 (p9-53): 数值例子 661 (p9-54): 特征向量的改进 664 (p9-55): 复共轭特征值 665 (p9-56): 重的和非常靠近的特征值 667 (p9-57): 对ACE程序的评述 670 (p9-58): 参考文献

This volume, which became a classic on first publication, is perhaps the most important and widely read book in the field of numerical analysis. It presents a distillation of the author's pioneering discoveries concerning the computation of matrix eigenvalues. The emphasis is on the transmission of knowledge rather than elaborate proofs. The book will be valued by all practising numerical analysts, students and researchers in the field, engineers, and scientists., Series: Numerical Mathematics and Scientific Computation, Issue: 14, Edition: 1, Bibliography: p. [649]-655, Includes index

Elementary introduction to problem of cumulative effect of rounding errors in a very large number of arithmetical calculations—particularly applicable to computer operations. Simple representative analyses illustrate techniques. Topics include fundamental arithmetic operations, computations involving polynomials and matrix computations. Results deal exclusively with digital computers but are equally applicable to desk calculators. Bibliography.<br

xv, 934 pages : 25 cm Previous edition: London : Hill, 1973 Includes index

This report, published November 11 by the National Confidential Enquiry into Patient Outcomes (NCEPOD), presents data from people over 80 years old who died within 30 days of operations done between April 1 and June 30, 2008. Data for all aspects of care, from admission to death, were gathered by review of 820 case notes and around 2000 questionnaires completed by the doctors involved in the patients' care. Other data on hospital services were gathered from 280 organisational questionnaires. The patients were operated on in all hospitals in England, Wales, Northern Ireland, the Isle of Man, and the Channel Islands

Advances in Microbial Physiology

Issue: до 2011-01, Includes index, Description based on print version record

1 online resource (x, 369 pages) :, Includes bibliographical references and index, Print version record

For each offence chapter, this provides an updated table of offences and penalties. It discusses many new cases including DPP v Shaw, it reproduces revised Magistrates' Association Suggestions for Traffic Offence Penalties, covers R v Bird (Simon) (aggravated vehicle taking) and other cases.

Clearly written and understandably organized, this classic book about European political, social, economic, and intellectual history covers events throughout the Continent from 1914 to the present, treating Europe as a single unit. This new edition features a thoroughly updated final chapter with the latest research on contemporary subjects. The author begins with a view of Europe in 1914 with an emphasis on Eastern Europe, Scandinavia, and the Mediterranean, as well as on Western Europe. The book thoroughly covers such contemporary topics as: the successful launch of the Euro as the currency of the European Union; the election of Vladimir Putin and the emergence of a new Russia; the election of Tony Blair and the rise of New Labor in the United Kingdom; the expansion of NATO; the rise of right-wing extremism; and the tense relations between Europeans and immigrant groups, particularly Muslims; all topics contribute to this being the leading source of information on this important and timely field. Coverage also includes: the First World War; the Russian Revolution and its consequences; technology and society; the high culture of the 1920s; the Great Depression; the Fascist regimes; the Stalinist system; the Second World War; the Cold War; the loss of Colonial Empire; achieving prosperity; and the future of a new Europe. For readers who wish to own a comprehensive and interesting book about the contemporary history of Europe; this book will also serve as an excellent reference for scholars of history or those who are involved in firms that trade internationally. -- Provided by Publisher --

413 p. 24cm

Advances in Microbial Physiology

<br> With the publication of his <b>Textbook of Dermatology</b>, the [late] Arthur Rook established it as the most comprehensive work of reference available to the dermatologist. Subsequent editions have been expanded as the subject has developed and the book remains the ultimate source of clinical information for the trainee and practising dermatologist alike. Two new editors (Drs Burns and Breathnach) have been brought to the team from complementary backgrounds in clinical practice and research. Dr Burns is a former editor of the British Journal of Dermatology. <br> The sixth edition contains three new chapters on epidemiology, molecular biology and wound healing. In addition, the chapter on physical and surgical therapies has been divided into two separate chapters to reflect the development of techniques such as laser treatment and chemical peels.

All you need to know about healthy living, living a healthy, balanced lifestyle - physical, spiritual, emotional and mental is much easier, and infinitely more rewarding than most people imagine. The key to reaching the goal is total wellness, which is what "Health 4 Life" is all about. Full of practical pointers and encouraging insights, this is a welcome resource for everyone who wants to achieve a balanced, healthy way of life. First Place users know the value of this resource and millions more will welcome its excellent health tips and practical eating helps. A full spectrum of wellness-related topics are covered - how to eat healthy while traveling or dining out; understanding and preventing cancer, heart disease and high cholesterol.

15p. ; 21cm Facsim of: A chapter from Lancashire legends. London : 1873

Clearly written and understandably organized, this classic book about European political, social, economic, and intellectual history covers events throughout the Continent from 1914 to the present, treating Europe as a single unit. This new edition features a thoroughly updated final chapter with the latest research on contemporary subjects. The author begins with a view of Europe in 1914 with an emphasis on Eastern Europe, Scandinavia, and the Mediterranean, as well as on Western Europe. The book thoroughly covers such contemporary topics as: the successful launch of the Euro as the currency of the European Union; the election of Vladimir Putin and the emergence of a new Russia; the election of Tony Blair and the rise of New Labor in the United Kingdom; the expansion of NATO; the rise of right-wing extremism; and the tense relations between Europeans and immigrant groups, particularly Muslims; all topics contribute to this being the leading source of information on this important and timely field. Coverage also includes: the First World War; the Russian Revolution and its consequences; technology and society; the high culture of the 1920s; the Great Depression; the Fascist regimes; the Stalinist system; the Second World War; the Cold War; the loss of Colonial Empire; achieving prosperity; and the future of a new Europe. For readers who wish to own a comprehensive and interesting book about the contemporary history of Europe; this book will also serve as an excellent reference for scholars of history or those who are involved in firms that trade internationally.

Advances in Microbial Physiology

Edition with English translation of a document shedding huge light on one of the most important figures of her time. The household roll of Eleanor, countess of Leicester and Pembroke, offers a fascinating insight into one of the most important domestic establishments in England during the Second Barons' War of 1263-7. As the wife of Simon de Montfort, earl of Leicester, the leading figure within the baronial regime, and the sister and aunt of King Henry III and the Lord Edward, respectively, Countess Eleanor occupied a position at the heart of English political affairs up to, and after, her husband's death at the Battle of Evesham on 4 August 1265. This volume is a critical edition of the extant thirteen membranes of Countess Eleanor's household account roll for that momentous year, 1265 (British Library, Additional MS 8877). Presented here in the original Latin and with an accompanying English translation, Countess Eleanor's roll includes her diet account for the period from 19 February to 29 August 1265, listing her visitors and the different items of food and drink consumed on each day at each castle at which she was resident, including Wallingford, Odiham and Dover. The roll also incorporates a "wardrobe journal", covering the period up until 1 October 1265, detailing expenditure on the purchase and repair of household furnishings, goods and utensils, on clothing and wages, on the Montfortian war effort in the South, and on messengers travelling to and from the countess, Earl Simon, her sons and associates, in the months before and after the Battle of Evesham.