内容太多感觉像是字典呢目录1 预备知识 (Preliminaries)1.1 精度与稳定性 (Accuracy and Stability)1.2 C 系列语言语法 (C Family Syntax)1.3 对象、类与继承 (Objects, Classes, and Inheritance)1.4 向量与矩阵对象 (Vector and Matrix Objects)1.5 更多约定与功能 (Some Further Conventions and Capabilities)2 线性代数方程组的求解 (Solution of Linear Algebraic Equations)2.0 引言 (Introduction)2.1 高斯-约当消元法 (Gauss-Jordan Elimination)2.2 带回代的高斯消元法 (Gaussian Elimination with Backsubstitution)2.3 LU 分解及其应用 (LU Decomposition and Its Applications)2.4 三对角与带状对角方程组 (Tridiagonal and Band-Diagonal Systems of Equations)2.5 线性方程组解的迭代改进 (Iterative Improvement of a Solution to Linear Equations)2.6 奇异值分解 (Singular Value Decomposition)2.7 稀疏线性方程组 (Sparse Linear Systems)2.8 范德蒙矩阵与托普利茨矩阵 (Vandermonde Matrices and Toeplitz Matrices)2.9 乔列斯基分解/柯列斯基分解 (Cholesky Decomposition)2.10 QR 分解 (QR Decomposition)2.11 矩阵求逆是一个N3N^3N3阶的过程吗 (Is Matrix Inversion anN3N^3N3Process?)3 插值与外推 (Interpolation and Extrapolation)3.0 引言 (Introduction)3.1 准备工作检索有序表 (Preliminaries: Searching an Ordered Table)3.2 多项式插值与外推 (Polynomial Interpolation and Extrapolation)3.3 三次样条插值 (Cubic Spline Interpolation)3.4 有理函数插值与外推 (Rational Function Interpolation and Extrapolation)3.5 插值多项式的系数 (Coefficients of the Interpolating Polynomial)3.6 多维网格插值 (Interpolation on a Grid in Multidimensions)3.7 多维散点数据插值 (Interpolation on Scattered Data in Multidimensions)3.8 拉普拉斯插值 (Laplace Interpolation)4 函数积分 / 数值积分 (Integration of Functions)4.0 引言 (Introduction)4.1 等距节点经典公式 (Classical Formulas for Equally Spaced Abscissas)4.2 初等算法 (Elementary Algorithms)4.3 龙贝格积分法 (Romberg Integration)4.4 反常积分 / 广义积分 (Improper Integrals)4.5 变量代换求积法 (Quadrature by Variable Transformation)4.6 高斯求积与正交多项式 (Gaussian Quadratures and Orthogonal Polynomials)4.7 自适应求积 (Adaptive Quadrature)4.8 多维积分 (Multidimensional Integrals)5 函数计算 (Evaluation of Functions)5.0 引言 (Introduction)5.1 多项式与有理函数 (Polynomials and Rational Functions)5.2 连分式计算 (Evaluation of Continued Fractions)5.3 级数及其收敛性 (Series and Their Convergence)5.4 递推关系与克兰肖递推公式 (Recurrence Relations and Clenshaw’s Recurrence Formula)5.5 复数运算 (Complex Arithmetic)5.6 一元二次与一元三次方程 (Quadratic and Cubic Equations)5.7 数值导数 / 数值微分 (Numerical Derivatives)5.8 切比雪夫逼近 (Chebyshev Approximation)5.9 切比雪夫逼近函数的导数或积分 (Derivatives or Integrals of a Chebyshev-Approximated Function)5.10 从切比雪夫系数推导多项式逼近 (Polynomial Approximation from Chebyshev Coefficients)5.11 幂级数的节约化 (Economization of Power Series)后面的没看5.12 帕德逼近 (Padé Approximants)5.13 有理切比雪夫逼近 (Rational Chebyshev Approximation)5.14 路径积分法计算函数 (Evaluation of Functions by Path Integration)6 特殊函数 (Special Functions)6.0 引言 (Introduction)6.1 伽马函数、贝塔函数、阶乘、二项式系数 (Gamma Function, Beta Function, Factorials, Binomial Coefficients)6.2 不完全伽马函数与误差函数 (Incomplete Gamma Function and Error Function)6.3 指数积分 (Exponential Integrals)6.4 不完全贝塔函数 (Incomplete Beta Function)6.5 整数阶贝塞尔函数 (Bessel Functions of Integer Order)6.6 分数阶贝塞尔函数、艾里函数、球贝塞尔函数 (Bessel Functions of Fractional Order, Airy Functions, Spherical Bessel Functions)6.7 球谐函数 (Spherical Harmonics)6.8 菲涅耳积分、余弦和正弦积分 (Fresnel Integrals, Cosine and Sine Integrals)6.9 道森积分 (Dawson’s Integral)6.10 广义费米-狄拉克积分 (Generalized Fermi-Dirac Integrals)6.11 函数xlog(x)x \log(x)xlog(x)的反函数 (Inverse of the Functionxlog(x)x \log(x)xlog(x))6.12 椭圆积分与雅可比椭圆函数 (Elliptic Integrals and Jacobian Elliptic Functions)6.13 超几何函数 (Hypergeometric Functions)6.14 统计学函数 (Statistical Functions)7 随机数 (Random Numbers)7.0 引言 (Introduction)7.1 均匀偏差 / 均匀随机数 (Uniform Deviates)7.2 大数组的完全哈希 (Completely Hashing a Large Array)7.3 其他分布的随机数 (Deviates from Other Distributions)7.4 多元正态随机数 (Multivariate Normal Deviates)7.5 线性反馈移位寄存器 (Linear Feedback Shift Registers)7.6 哈希表与哈希存储 (Hash Tables and Hash Memories)7.7 简单蒙特卡罗积分 (Simple Monte Carlo Integration)7.8 准随机序列 / 低偏差序列 (Quasi- or Sub-Random Sequences)7.9 自适应与递归蒙特卡罗方法 (Adaptive and Recursive Monte Carlo Methods)8 排序与选择 (Sorting and Selection)8.0 引言 (Introduction)8.1 直接插入排序与希尔排序 (Straight Insertion and Shell’s Method)8.2 快速排序 (Quicksort)8.3 堆排序 (Heapsort)8.4 索引与排行 (Indexing and Ranking)8.5 选择第 M 大的数 (Selecting the Mth Largest)8.6 等价类的确定 (Determination of Equivalence Classes)9 求根与非线性方程组 (Root Finding and Nonlinear Sets of Equations)9.0 引言 (Introduction)9.1 区间套法与二分法 (Bracketing and Bisection)9.2 割线法、试位法与里德斯方法 (Secant Method, False Position Method, and Ridders’ Method)9.3 范韦恩加登-德克尔-布伦特方法 / Brent 方法 (Van Wijngaarden-Dekker-Brent Method)9.4 利用导数的牛顿-拉夫逊方法 (Newton-Raphson Method Using Derivative)9.5 多项式的根 (Roots of Polynomials)9.6 非线性方程组的牛顿-拉夫逊方法 (Newton-Raphson Method for Nonlinear Systems of Equations)9.7 非线性方程组的全局收敛方法 (Globally Convergent Methods for Nonlinear Systems of Equations)10 函数的极值优化微积分极值 (Minimization or Maximization of Functions)10.0 引言 (Introduction)10.1 极值区间的初始确定 (Initially Bracketing a Minimum)10.2 一维黄金分割搜索法 (Golden Section Search in One Dimension)10.3 一维抛物线插值与 Brent 方法 (Parabolic Interpolation and Brent’s Method in One Dimension)10.4 利用一阶导数的一维搜索 (One-Dimensional Search with First Derivatives)10.5 多维下山单纯形法 (Downhill Simplex Method in Multidimensions)10.6 多维线搜索方法 (Line Methods in Multidimensions)10.7 多维方向集方法 / 鲍威尔方法 (Direction Set (Powell’s) Methods in Multidimensions)10.8 多维共轭梯度法 (Conjugate Gradient Methods in Multidimensions)10.9 多维拟牛顿法或变尺度法 (Quasi-Newton or Variable Metric Methods in Multidimensions)10.10 线性规划单纯形法 (Linear Programming: The Simplex Method)10.11 线性规划内点法 (Linear Programming: Interior-Point Methods)10.12 模拟退火算法 (Simulated Annealing Methods)10.13 动态规划 (Dynamic Programming)11 特征值系统 (Eigensystems)11.0 引言 (Introduction)11.1 对称矩阵的雅可比变换 (Jacobi Transformations of a Symmetric Matrix)11.2 实对称矩阵 (Real Symmetric Matrices)11.3 对称矩阵转化为三对角形式吉文斯与豪斯霍尔德变换 (Reduction of a Symmetric Matrix to Tridiagonal Form: Givens and Householder Reductions)11.4 三对角矩阵的特征值与特征向量 (Eigenvalues and Eigenvectors of a Tridiagonal Matrix)11.5 埃尔米特矩阵 / 复自伴矩阵 (Hermitian Matrices)11.6 实非对称矩阵 (Real Nonsymmetric Matrices)11.7 实黑塞伯格矩阵的 QR 算法 (The QR Algorithm for Real Hessenberg Matrices)11.8 通过逆迭代改进特征值和/或寻找特征向量 (Improving Eigenvalues and/or Finding Eigenvectors by Inverse Iteration)12 快速傅里叶变换 (Fast Fourier Transform)12.0 引言 (Introduction)12.1 离散采样数据的傅里叶变换 (Fourier Transform of Discretely Sampled Data)12.2 快速傅里叶变换 (FFT) (Fast Fourier Transform (FFT))12.3 实函数的 FFT (FFT of Real Functions)12.4 快速正弦和余弦变换 (Fast Sine and Cosine Transforms)12.5 二维或多维 FFT (FFT in Two or More Dimensions)12.6 二维和三维实数据傅里叶变换 (Fourier Transforms of Real Data in Two and Three Dimensions)12.7 外部存储或局部内存 FFT (External Storage or Memory-Local FFTs)13 傅里叶与谱应用 (Fourier and Spectral Applications)13.0 引言 (Introduction)13.1 利用 FFT 进行卷积与解卷 (Convolution and Deconvolution Using the FFT)13.2 利用 FFT 进行相关与自相关 (Correlation and Autocorrelation Using the FFT)13.3 利用 FFT 进行最佳维纳滤波 (Optimal (Wiener) Filtering with the FFT)13.4 利用 FFT 进行功率谱估计 (Power Spectrum Estimation Using the FFT)13.5 时域数字滤波 (Digital Filtering in the Time Domain)13.6 线性预测与线性预测编码 (Linear Prediction and Linear Predictive Coding)13.7 基于最大熵全极点法的功率谱估计 (Power Spectrum Estimation by the Maximum Entropy (All-Poles) Method)13.8 非均匀采样数据的光谱分析 (Spectral Analysis of Unevenly Sampled Data)13.9 利用 FFT 计算傅里叶积分 (Computing Fourier Integrals Using the FFT)13.10 小波变换 (Wavelet Transforms)13.11 采样定理的数值应用 (Numerical Use of the Sampling Theorem)14 数据的统计描述 (Statistical Description of Data)14.0 引言 (Introduction)14.1 分布的矩均值、方差、偏度等 (Moments of a Distribution: Mean, Variance, Skewness, and So Forth)14.2 两个分布的均值或方差是否相同 (Do Two Distributions Haveethe Same Means or Variances?)14.3 两个分布是否不同 (Are Two Distributions Different?)14.4 两个分布的列联表分析 (Contingency Table Analysis of Two Distributions)14.5 线性相关 (Linear Correlation)14.6 非参数或秩相关 (Nonparametric or Rank Correlation)14.7 分布的信息论性质 (Information-Theoretic Properties of Distributions)14.8 二维分布是否有差异 (Do Two-Dimensional Distributions Differ?)14.9 萨维茨基-戈莱平滑滤波器 (Savitzky-Golay Smoothing Filters)15 数据建模 (Modeling of Data)15.0 引言 (Introduction)15.1 最小二乘法作为最大似然估计器 (Least Squares as a Maximum Likelihood Estimator)15.2 拟合数据到直线 (Fitting Data to a Straight Line)15.3 两个坐标均有误差的直线数据拟合 (Straight-Line Data with Errors in Both Coordinates)15.4 一般线性最小二乘法 (General Linear Least Squares)15.5 非线性模型拟合 (Nonlinear Models)15.6 估计模型参数的置信区间 (Confidence Limits on Estimated Model Parameters)15.7 稳健估计 / 鲁棒估计 (Robust Estimation)15.8 马尔可夫链蒙特卡罗法 (MCMC) (Markov Chain Monte Carlo)15.9 高斯过程回归 (Gaussian Process Regression)16 分类与推断 (Classification and Inference)16.0 引言 (Introduction)16.1 高斯混合模型与 K-均值聚类 (Gaussian Mixture Models and k-Means Clustering)16.2 维特比解码 (Viterbi Decoding)16.3 马尔可夫模型与隐马尔可夫模型 (MHM) (Markov Models and Hidden Markov Modeling)16.4 基于系统发育树的分层聚类 (Hierarchical Clustering by Phylogenetic Trees)16.5 支持向量机 (SVM) (Support Vector Machines)17 常微分方程的积分 / 数值解法 (Integration of Ordinary Differential Equations)17.0 引言 (Introduction)17.1 龙格-库塔法 (Runge-Kutta Method)17.2 龙格-库塔法的自适应步长控制 (Adaptive Stepsize Control for Runge-Kutta)17.3 理查森外推法与 Bulirsch-Stoer 方法 (Richardson Extrapolation and the Bulirsch-Stoer Method)17.4 二阶保守方程 (Second-Order Conservative Equations)17.5 刚性方程组 (Stiff Sets of Equations)17.6 多步、多值和预测-校正方法 (Multistep, Multivalue, and Predictor-Corrector Methods)17.7 化学反应网络的随机模拟 (Stochastic Simulation of Chemical Reaction Networks)18 两点边值问题 (Two-Point Boundary Value Problems)18.0 引言 (Introduction)18.1 打靶法 (The Shooting Method)18.2 匹配点打靶法 (Shooting to a Fitting Point)18.3 松弛法 (Relaxation Methods)18.4 实例解析类球面谐函数 (A Worked Example: Spheroidal Harmonics)18.5 网格点的自动分配 (Automated Allocation of Mesh Points)18.6 内部边界条件或奇异点的处理 (Handling Internal Boundary Conditions or Singular Points)19 积分方程与反演理论 (Integral Equations and Inverse Theory)19.0 引言 (Introduction)19.1 第二类弗雷德霍姆方程 (Fredholm Equations of the Second Kind)19.2 沃尔泰拉方程 (Volterra Equations)19.3 具有奇异核的积分方程 (Integral Equations with Singular Kernels)19.4 反问题与先验信息的使用 (Inverse Problems and the Use of A Priori Information)19.5 线性正则化方法 (Linear Regularization Methods)19.6 巴克斯-吉尔伯特方法 (Backus-Gilbert Method)19.7 最大熵图像恢复 (Maximum Entropy Image Restoration)20 偏微分方程 (Partial Differential Equations)20.0 引言 (Introduction)20.1 通量守恒型初值问题 (Flux-Conservative Initial Value Problems)20.2 扩散型初值问题 (Diffusive Initial Value Problems)20.3 多维初值问题 (Initial Value Problems in Multidimensions)20.4 边界值问题的傅里叶法与循环削减法 (Fourier and Cyclic Reduction Methods for Boundary Value Problems)20.5 边界值问题的松弛法 (Relaxation Methods for Boundary Value Problems)20.6 边界值问题的多网格法 (Multigrid Methods for Boundary Value Problems)20.7 谱方法 (Spectral Methods)21 计算几何 (Computational Geometry)21.0 引言 (Introduction)21.1 点与包围盒 (Points and Boxes)21.2 KD 树与 nearest-neighbor 查找 (KD Trees and Nearest-Neighbor Finding)21.3 二维与三维空间中的三角形 (Triangles in Two and Three Dimensions)21.4 直线、线段与多边形 (Lines, Line Segments, and Polygons)21.5 球体与旋转 (Spheres and Rotations)21.6 三角剖分与德劳内三角剖分 (Triangulation and Delaunay Triangulation)21.7 德劳内三角剖分的应用 (Applications of Delaunay Triangulation)21.8 四叉树与八叉树几何对象的存储 (Quadtrees and Octrees: Storing Geometrical Objects)22 弱数值算法 / 离散算法 (Less-Numerical Algorithms)22.0 引言 (Introduction)22.1 简单图表的绘制 (Plotting Simple Graphs)22.2 机器参数的诊断 (Diagnosing Machine Parameters)22.3 格雷码 (Gray Codes)22.4 循环冗余校验与其它校验和 (Cyclic Redundancy and Other Checksums)22.5 霍夫曼编码与数据压缩 (Huffman Coding and Compression of Data)22.6 算术编码 (Arithmetic Coding)22.7 任意精度算术运算 / 大数运算 (Arithmetic at Arbitrary Precision)索引 (Index)
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