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| Burden R.L., Faires J.D. — Numerical analysis |
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| Предметный указатель |
Heat flow in a rod 624
Hermite Interpolation Algorithm 128
Hermite piecewise cubic polynomial 131 150 251
Hermite polynomial 91 123
Heun method 258
Higher-order differential equation 294
Hilbert matrix 433 451
History problem 247
Homotopy method 575
Hooke's law 435 445
Horner's algorithm 84
Horner's method 83
Hotelling deflation 521
Householder algorithm 526
Householder method 523
Householder transformation 523
Hyperbolic partial-differential equation 624 649
Ideal gas law 1 24
Identity matrix 348
Ill-conditioned matrix 426
Implicit method 181 271
Improper integral 224
IMSL 37
Induced matrix norm 397
Initial-value problem, A-stable method 317
Initial-value problem, Adams Predictor-Corrector Algorithm 279
Initial-value problem, Adams Variable Step-Size Predictor-Corrector Algorithm 284
Initial-value problem, Adams — Bashforth method 275
Initial-value problem, Adams — Moulton method 276
Initial-value problem, characteristic polynomial 309
Initial-value problem, consistent method 304 308
Initial-value problem, convergent method 304 309
Initial-value problem, definition 234
Initial-value problem, error control 263 282
Initial-value problem, Euler Algorithm 240
Initial-value problem, Extrapolation Algorithm 290
Initial-value problem, Heun method 258
Initial-value problem, local truncation error 248 274
Initial-value problem, midpoint method 257
Initial-value problem, Milne method 280
Initial-value problem, Milne — Simpson method 280
Initial-value problem, modified Euler method 257
Initial-value problem, multistep method 270
Initial-value problem, perturbation 236
Initial-value problem, predictor-corrector method 278
Initial-value problem, region of absolute stability 317
Initial-value problem, root condition 311
Initial-value problem, Runge — Kutta Order Four Algorithm 259
Initial-value problem, Runge — Kutta Order Four for Systems Algorithm 297
Initial-value problem, Runge — Kutta order two 257
Initial-value problem, Runge — Kutta — Fehlberg Algorithm 266
Initial-value problem, Simpson method 280
Initial-value problem, stiff equation 314
Initial-value problem, strong stability 311
Initial-value problem, Taylor method 249
Initial-value problem, Trapezoidal Method with Newton Iteration Algorithm 318
Initial-value problem, weak stability 311
Initial-value problem, well-posed problem 236
Integral, improper 224
Integral, Riemann 5
Integration see "Numerical integration"
Intermediate Value Theorem 7
Interpolation using zeros of Chebyshev polynomials 464
Interpolation, cubic spline 132
Interpolation, description 96
Interpolation, Hermite polynomial 123
Interpolation, inverse 110
Interpolation, iterated inverse 110
Interpolation, Lagrange polynomial 98
Interpolation, Neville method 106
Interpolation, Taylor polynomial 97
Inverse matrix 349
Inverse power method 513
Inverse Power Method Algorithm 515
Isotropic 622
Iterated inverse interpolation 110
Iterative refinement 424
Iterative Refinement Algorithm 429
ITPACK 434
Jacobi Iterative Algorithm 409
Jacobi iterative method 408
Jacobi method for a symmetric matrix 539
Jacobian matrix 555
Jenkins — Traub method 94
Kahan's theorem 417
Kentucky Derby problem 146
Kirchhoff's laws 167 247 288 297 323
Lagrange polynomial definition 100
Lagrange polynomial, recursively generating 105
Laguerre method 94
Laguerre polynomial 91 229 459
LAPACK 37
Laplace equation 623
Laplace equation on a rectangle 565
Leading principal submatrix 370
Least squares, continuous 449
Least squares, discrete 436
Least squares, exponential 442
Least squares, general 440
Least squares, linear 438
Least-change secant update method 561
Legendre polynomial 207 457
Levenberg Marquardt method 576
Life-expectancy problem 448 567
Limit of a function 2 546
Limit of a sequence 2 394
Linear basis functions 607
Linear boundary-value problem 578
Linear Finite-Difference Algorithm 594
Linear Shooting Algorithm 580
Linear shooting method 578
Linear system definition 324
Linear system reduced form 328 348 362
Linear system triangular form 328 348 362
Linear system, backward substitution 325
Linearly dependent functions 451
Linearly dependent vectors 498
Linearly independent eigenvectors 500
Linearly independent functions 451
Linearly independent vectors 498
LINPACK 36 387 434
Lipschitz condition 12 234 295
Lipschitz constant 12 234
Local truncation error, multistep method 274
Local truncation error, one-step method 248
Local truncation error, related to global error 305
Logistic population growth 294
Long real 14
Lower triangular matrix 348 362
Machine number 13
Maclaurin polynomial 8
Maclaurin series 8
Macsyma 38
Mantissa 13
Maple 38
Mathematica 38
MATLAB 38
Matrix definition 325
Matrix identity 348
Matrix Jacobian 555
Matrix norm 396
Matrix rotation 531
Matrix,  Algorithm 376
Matrix,  norm 400
Matrix,  norm 397 403
Matrix,  norm 397
Matrix, addition 346
Matrix, augmented 326
Matrix, band 379
Matrix, block tridiagonal 384
| Matrix, Choleski's Algorithm 376
Matrix, convergent 404
Matrix, Croat Reduction for Tridiagonal Linear Systems Algorithm 380
Matrix, determinant 358
Matrix, diagonal 348
Matrix, Direct Factorization Algorithm 366
Matrix, equal 345
Matrix, factorization 362
Matrix, Frobenius norm 400
Matrix, Gauss transformation 363
Matrix, Gauss — Jordan method 336
Matrix, Gauss — Seidel Iterative Algorithm 411
Matrix, Gaussian Elimination with Backward Substitution Algorithm 330
Matrix, Hilbert 433 451
Matrix, ill-conditioned 426
Matrix, inverse 349
Matrix, Iterative Refinement Algorithm 429
Matrix, Jacobi Iterative Algorithm 409
Matrix, lower triangular 348 362
Matrix, Maximal Column Pivoting Algorithm 340
Matrix, minor 358
Matrix, multiplication 347
Matrix, nonsingular 349
Matrix, null 348
Matrix, orthogonal 500
Matrix, partitioned tridiagonal 384
Matrix, permutation 367
Matrix, persymmetric 505
Matrix, pivoting 340
Matrix, positive definite 373 423 502
Matrix, product 347
Matrix, reduced to diagonal 510
Matrix, reduced to tridiagonal 523
Matrix, scalar multiplication 346
Matrix, Scaled Column Pivoting Algorithm 343
Matrix, similar 500
Matrix, singular 349
Matrix, SOR Algorithm 418
Matrix, sparse 390
Matrix, square 348
Matrix, strictly diagonally dominant 371
Matrix, submatrix 358
Matrix, sum 346
Matrix, symmetry 353
Matrix, transpose 353
Matrix, tridiagonal 379
Matrix, tridiagonal block 384
Matrix, unitary 501
Matrix, upper Hessenberg 529 537
Matrix, upper triangular 348 362
Matrix, well-conditioned 426
Matrix, zero 348
Maximal column pivoting 340
Maximal pivoting 344
Mean value theorem 5
Mean Value Theorem for Integrals 6
Mesh points 239 626
Method of collocation 618
Method of false position 63
Method of False Position Algorithm 64
Midpoint method 257
Midpoint rule 182
Midpoint rule, composite 188
Milne method 280
Milne — Simpson method 280
minimax 437
Minor 358
Modified Euler method 257
Monic polynomial 462
Mueller's Algorithm 88
Mueller's method 87
Multiple integrals 211
Multiplicity of a root 73
Multistep method 270
NAG 37
Natural boundary 133
Natural Cubic Spline Algorithm 136
Natural matrix norm 397
Natural spline 133
Nested arithmetic 20
Neville's Iterated Interpolation Algorithm 108
Newton backward difference formula 116
Newton backward divided-difference formula 116
Newton forward divided-difference formula 116
Newton forward-difference formula 116
Newton interpolatory divided-difference formula 113
Newton — Cotes closed formula 179
Newton — Cotes open formula 181
Newton — Raphson algorithm 57
Newton — Raphson method see "Newton's method"
Newton's method algorithm 57
Newton's method definition 56
Newton's method description 57
Newton's method for nonlinear boundary-value problem 587
Newton's method for stiff equation 318
Newton's method for systems 555
Newton's Method for Systems Algorithm 555
Newton's method, convergence criteria 60
Newton's method, modified for multiple roots 75 77
Newton's method, quadratic convergence of 60
Noble beast problem 147
nodes 133 659
Nonlinear Finite-Difference Algorithm 601
Nonlinear Shooting Algorithm 588
Nonsingular matrix 349
Norm of a matrix definition 396
Norm of a matrix, 400
Norm of a matrix, 397 403
Norm of a matrix, 397
Norm of a matrix, Frobenius 400
Norm of a vector definition 390
Norm of a vector, 399
Norm of a vector, 391
Norm of a vector, 391
Norm of a vector, algorithm 33
Normal equations 438 440 450
Null matrix 348
Numerical differentiation description 157
Numerical differentiation, backward-difference formula 158
Numerical differentiation, five-point formula 161
Numerical differentiation, forward-difference formula 158
Numerical differentiation, higher derivatives 162
Numerical differentiation, instability 165
Numerical differentiation, Richardson extrapolation 168
Numerical differentiation, round-off error 165
Numerical differentiation, three-point formula 161
Numerical integration, adaptive quadrature 192
Numerical integration, closed formula 179
Numerical integration, composite midpoint rule 188
Numerical integration, composite Simpson's rule 186
Numerical integration, composite trapezoidal rule 187
Numerical integration, double integral 211
Numerical integration, explicit formula 179
Numerical integration, Gaussian quadrature 205 214
Numerical integration, implicit formula 181
Numerical integration, improper integral 224
Numerical integration, midpoint rule 182
Numerical integration, multiple integral 211
Numerical integration, open formula 181
Numerical integration, Romberg 199
Numerical integration, Simpson's rule 175
Numerical integration, stability 189
Numerical integration, Trapezoidal rule 175
Numerical integration, triple integral 219
Numerical quadrature see "Numerical integration"
Numerical software 32
o notation 29
Oak leaves problem 146
Open method 271 see
Open Newton — Cotes formula 181
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