| Preface to the C++ Edition |
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xi | |
| Preface to the Second Edition |
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xii | |
| Preface to the First Edition |
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xv | |
| License Information |
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xvii | |
| Computer Programs by Chapter and Section |
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xxi | |
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1 | (34) |
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1 | (4) |
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Program Organization and Control Structures |
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5 | (11) |
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Some C++ Conventions for Scientific Computing |
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16 | (9) |
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Implementation of the Vector and Matrix Classes |
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25 | (6) |
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Error, Accuracy, and Stability |
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31 | (4) |
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Solution of Linear Algebraic Equations |
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35 | (73) |
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35 | (4) |
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39 | (5) |
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Gaussian Elimination with Backsubstitution |
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44 | (2) |
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LU Decomposition and Its Applications |
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46 | (7) |
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Tridiagonal and Band Diagonal Systems of Equations |
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53 | (5) |
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Iterative Improvement of a Solution to Linear Equations |
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58 | (4) |
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Singular Value Decomposition |
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62 | (12) |
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74 | (19) |
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Vandermonde Matrices and Toeplitz Matrices |
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93 | (6) |
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99 | (2) |
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101 | (4) |
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Is Matrix Inversion an N3 Process? |
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105 | (3) |
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Interpolation and Extrapolation |
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108 | (25) |
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108 | (3) |
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Polynomial Interpolation and Extrapolation |
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111 | (3) |
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Rational Function Interpolation and Extrapolation |
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114 | (2) |
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Cubic Spline Interpolation |
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116 | (4) |
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How to Search an Ordered Table |
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120 | (3) |
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Coefficients of the Interpolating Polynomial |
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123 | (3) |
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Interpolation in Two or More Dimensions |
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126 | (7) |
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133 | (38) |
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133 | (1) |
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Classical Formulas for Equally Spaced Abscissas |
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134 | (7) |
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141 | (3) |
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144 | (2) |
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146 | (6) |
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Gaussian Quadratures and Orthogonal Polynomials |
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152 | (14) |
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Multidimensional Integrals |
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166 | (5) |
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171 | (46) |
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171 | (1) |
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Series and Their Convergence |
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171 | (4) |
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Evaluation of Continued Fractions |
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175 | (4) |
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Polynomials and Rational Functions |
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179 | (3) |
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182 | (2) |
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Recurrence Relations and Clenshaw's Recurrence Formula |
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184 | (5) |
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Quadratic and Cubic Equations |
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189 | (3) |
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192 | (4) |
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196 | (5) |
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Derivatives or Integrals of a Chebyshev-approximated Function |
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201 | (2) |
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Polynomial Approximation from Chebyshev Coefficients |
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203 | (1) |
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Economization of Power Series |
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204 | (2) |
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206 | (3) |
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Rational Chebyshev Approximation |
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209 | (4) |
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Evaluation of Functions by Path Integration |
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213 | (4) |
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217 | (61) |
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217 | (1) |
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Gamma Function, Beta Function, Factorials, Binomial Coefficients |
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218 | (3) |
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Incomplete Gamma Function, Error Function, Chi-Square Probability Function, Cumulative Poisson Function |
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221 | (6) |
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227 | (4) |
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Incomplete Beta Function, Student's Distribution, F-Distribution, Cumulative Binomial Distribution |
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231 | (4) |
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Bessel Functions of Integer Order |
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235 | (6) |
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Modified Bessel Functions of Integer Order |
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241 | (4) |
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Bessel Functions of Fractional Order, Airy Functions, Spherical Bessel Functions |
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245 | (12) |
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257 | (2) |
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Fresnel Integrals, Cosine and Sine Integrals |
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259 | (5) |
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264 | (1) |
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Elliptic Integrals and Jacobian Elliptic Functions |
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265 | (10) |
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275 | (3) |
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278 | (54) |
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278 | (1) |
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279 | (12) |
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Transformation Method: Exponential and Normal Deviates |
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291 | (3) |
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Rejection Method: Gamma, Poisson, Binomial Deviates |
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294 | (6) |
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Generation of Random Bits |
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300 | (4) |
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Random Sequences Based on Data Encryption |
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304 | (4) |
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Simple Monte Carlo Integration |
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308 | (5) |
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Quasi- (that is, Sub-) Random Sequences |
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313 | (7) |
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Adaptive and Recursive Monte Carlo Methods |
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320 | (12) |
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332 | (19) |
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332 | (1) |
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Straight Insertion and Shell's Method |
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333 | (3) |
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336 | (3) |
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339 | (2) |
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341 | (3) |
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Selecting the Mth Largest |
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344 | (4) |
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Determination of Equivalence Classes |
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348 | (3) |
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Root Finding and Nonlinear Sets of Equations |
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351 | (47) |
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351 | (3) |
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354 | (4) |
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Secant Method, False Position Method, and Ridders' Method |
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358 | (5) |
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Van Wijngaarden-Dekker-Brent Method |
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363 | (3) |
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Newton-Raphson Method Using Derivative |
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366 | (7) |
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373 | (10) |
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Newton-Raphson Method for Nonlinear Systems of Equations |
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383 | (4) |
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Globally Convergent Methods for Nonlinear Systems of Equations |
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387 | (11) |
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Minimization or Maximization of Functions |
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398 | (63) |
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398 | (3) |
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Golden Section Search in One Dimension |
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401 | (5) |
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Parabolic Interpolation and Brent's Method in One Dimension |
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406 | (4) |
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One-Dimensional Search with First Derivatives |
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410 | (3) |
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Downhill Simplex Method in Multidimensions |
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413 | (4) |
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Direction Set (Powell's) Methods in Multidimensions |
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417 | (7) |
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Conjugate Gradient Methods in Multidimensions |
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424 | (6) |
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Variable Metric Methods in Multidimensions |
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430 | (4) |
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Linear Programming and the Simplex Method |
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434 | (14) |
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Simulated Annealing Methods |
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448 | (13) |
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461 | (40) |
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461 | (7) |
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Jacobi Transformations of a Symmetric Matrix |
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468 | (6) |
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Reduction of a Symmetric Matrix to Tridiagonal Form: Givens and Householder Reductions |
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474 | (7) |
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Eigenvalues and Eigenvectors of a Tridiagonal Matrix |
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481 | (5) |
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486 | (1) |
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Reduction of a General Matrix to Hessenberg Form |
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487 | (4) |
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The QR Algorithm for Real Hessenberg Matrices |
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491 | (7) |
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Improving Eigenvalues and/or Finding Eigenvectors by Inverse Iteration |
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498 | (3) |
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501 | (41) |
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501 | (4) |
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Fourier Transform of Discretely Sampled Data |
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505 | (4) |
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Fast Fourier Transform (FFT) |
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509 | (6) |
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FFT of Real Functions, Sine and Cosine Transforms |
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515 | (11) |
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FFT in Two or More Dimensions |
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526 | (4) |
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Fourier Transforms of Real Data in Two and Three Dimensions |
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530 | (6) |
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External Storage or Memory-Local FFTs |
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536 | (6) |
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Fourier and Spectral Applications |
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542 | (72) |
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542 | (1) |
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Convolution and Deconvolution Using the FFT |
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543 | (7) |
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Correlation and Autocorrelation Using the FFT |
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550 | (2) |
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Optimal (Wiener) Filtering with the FFT |
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552 | (3) |
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Power Spectrum Estimation Using the FFT |
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555 | (8) |
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Digital Filtering in the Time Domain |
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563 | (6) |
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Linear Prediction and Linear Predictive Coding |
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569 | (8) |
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Power Spectrum Estimation by the Maximum Entropy (All Poles) Method |
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577 | (3) |
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Spectral Analysis of Unevenly Sampled Data |
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580 | (9) |
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Computing Fourier Integrals Using the FFT |
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589 | (7) |
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596 | (15) |
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Numerical Use of the Sampling Theorem |
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611 | (3) |
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Statistical Description of Data |
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614 | (47) |
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614 | (1) |
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Moments of a Distribution: Mean, Variance, Skewness, and So Forth |
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615 | (5) |
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Do Two Distributions Have the Same Means or Variances? |
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620 | (5) |
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Are Two Distributions Different? |
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625 | (8) |
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Contingency Table Analysis of Two Distributions |
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633 | (8) |
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641 | (3) |
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Nonparametric or Rank Correlation |
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644 | (6) |
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Do Two-Dimensional Distributions Differ? |
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650 | (5) |
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Savitzky-Golay Smoothing Filters |
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655 | (6) |
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661 | (51) |
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661 | (1) |
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Least Squares as a Maximum Likelihood Estimator |
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662 | (4) |
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Fitting Data to a Straight Line |
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666 | (5) |
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Straight-Line Data with Errors in Both Coordinates |
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671 | (5) |
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General Linear Least Squares |
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676 | (10) |
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686 | (8) |
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Confidence Limits on Estimated Model Parameters |
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694 | (10) |
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704 | (8) |
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Integration of Ordinary Differential Equations |
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712 | (44) |
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712 | (3) |
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715 | (4) |
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Adaptive Stepsize Control for Runge-Kutta |
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719 | (8) |
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727 | (2) |
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Richardson Extrapolation and the Bulirsch-Stoer Method |
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729 | (8) |
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Second-Order Conservative Equations |
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737 | (2) |
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739 | (12) |
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Multistep, Multivalue, and Predictor-Corrector Methods |
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751 | (5) |
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Two Point Boundary Value Problems |
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756 | (34) |
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756 | (4) |
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760 | (2) |
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Shooting to a Fitting Point |
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762 | (3) |
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765 | (10) |
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A Worked Example: Spheroidal Harmonics |
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775 | (10) |
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Automated Allocation of Mesh Points |
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785 | (2) |
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Handling Internal Boundary Conditions or Singular Points |
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787 | (3) |
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Integral Equations and Inverse Theory |
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790 | (39) |
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790 | (3) |
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Fredholm Equations of the Second Kind |
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793 | (3) |
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796 | (3) |
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Integral Equations with Singular Kernels |
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799 | (7) |
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Inverse Problems and the Use of A Priori Information |
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806 | (5) |
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Linear Regularization Methods |
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811 | (7) |
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818 | (3) |
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Maximum Entropy Image Restoration |
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821 | (8) |
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Partial Differential Equations |
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829 | (62) |
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829 | (7) |
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Flux-Conservative Initial Value Problems |
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836 | (13) |
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Diffusive Initial Value Problems |
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849 | (6) |
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Initial Value Problems in Multidimensions |
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855 | (4) |
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Fourier and Cyclic Reduction Methods for Boundary Value Problems |
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859 | (6) |
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Relaxation Methods for Boundary Value Problems |
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865 | (8) |
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Multigrid Methods for Boundary Value Problems |
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873 | (18) |
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Less-Numerical Algorithms |
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891 | (36) |
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891 | (1) |
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Diagnosing Machine Parameters |
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891 | (5) |
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896 | (2) |
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Cyclic Redundancy and Other Checksums |
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898 | (8) |
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Huffman Coding and Compression of Data |
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906 | (6) |
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912 | (4) |
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Arithmetic at Arbitrary Precision |
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916 | (11) |
| References |
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927 | (4) |
| Appendix A: Table of Function Declarations |
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931 | (8) |
| Appendix B: Utility Routines and Classes |
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939 | (18) |
| Appendix C: Converting to Single Precision |
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957 | (2) |
| Index of Programs and Dependencies |
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959 | (13) |
| General Index |
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972 | |