Minimum methods with first derivatives 467
Minimum methods without derivatives 464
Minimum methods, downhill 451
Minimum methods, ray minimum 452
Minimum path through a network 504f.
Minimum spanning tree for a network 516
Minimum term of asymptotic series 17 263
Multiple eigenvalues 339
Multiple roots 75
Multiple roots, indeterminacy near 76
Multiple roots, precision in calculating 76
Multiple roots, rate of convergence to 77
Multiple roots, speeding convergence near 77
Multiple roots, suppression of known roots near 78
Nearly multiple roots 78
Negligible terms of cubics (quartics, quadratics) 59
Neighborhood array 501
Network equations from the topology 520
Network flows, circuit equations for 519
Network flows, nodal equations for 519
Newton — Cotes quadrature 102
Newton — Cotes quadrature, rate of convergence 106
Newton's method 51
Newton's method for double polynomial roots 186
Newton's method for double roots 64
Newton's method for quadratic polynomial factors 194
Newton's method for second-order boundary-value problems in ordinary differential equations 175—176
Newton's method for simple polynomial roots 180
Newton's method, in n dimensions 367
Newton's method, in two dimensions 194 369
Newton's method, one-dimensional, in n-space 369
Newton's method, rate of convergence of 54
Newton's method, utility of, in higher dimensions 366
Nodal matrix for a network 501
Noise amplifier 439
Noise amplifier, suppressor 440
Non-polynomic behavior, need for removing 120
Nonlinear differential equations, linearization of 172
Normalization, of homogeneous equations 208
Normalization, of orthogonal functions 229
Normalization, of vectors 208 213
Numerical indeterminacy 76
Ordinary differential equations, boundary value problems Chapter 6
Ordinary differential equations, initial value problems Chapter 5
Ordinary differential equations, initial value problems, instabilities in numerical integration 143
Ordinary differential equations, initial value problems, Milne's method 132 see
Ordinary differential equations, initial value problems, predictor corrector methods 130
Ordinary differential equations, initial value problems, Runge — Kutta methods 139
Ordinary differential equations, mildly nonlinear systems 171
Ordinary differential equations, treated as initial-value problems 173
Orthogonal expansions, least-squares property of 224
Orthogonal functions, evaluating series of 11
Orthogonal polynomials on a discrete set of points 235
Orthogonal reductions of matrices to Hessenberg form 340f.
Orthogonal reductions of matrices to tridiagonal form 325
Orthogonality in Fourier series 223
Orthogonality of the eigenvectors of symmetric matrices 211
Orthogonalizing a vector with respect to another 219 380
Oscillatory infinite integrals 117
Parabolic partial differential equations 437f.
Parabolic partial differential equations, backward difference algorithms 442
Parabolic partial differential equations, forward difference algorithms 438
Parabolic partial differential equations, symmetric difference algorithms 445 446
Parallel plate condenser 491f.
Parallel plate condenser, conformal map for 494 497
Parallel plate condenser, Fourier series solution for 495
Parallel plate condenser, singular integral equation for 420 493
Pathologic polynomials 201
PERT 508f.
Perverse formulations of numerical problems 248
Pivoting see "Interchanging"
Plane rotations for matrices 319
Polynomial derivative evaluation, by synthetic division 183
Polynomial derivative evaluation, from tridiagonal form 234
Polynomial division 190
Polynomial evaluation, by synthetic division 59 181
Polynomial evaluation, from Hessenberg form 344
Polynomial evaluation, from tridiagonal form 332
Polynomial roots Chapter 7
Polynomial roots, shifting by a constant 59
Polynomials orthogonal on a discrete set of points 235
Position vector 210
Powell 458 464 467
Power method for eigenvalues see "Iterated multiplication"
Power series, from a continued fraction 285
Power series, from differential equations 15 269
Power series, from rational functions 282
Predecessor vectors 524
Predictor-corrector methods 130
Predictor-corrector methods for first order equations 130
Predictor-corrector methods for higher order equations 140
Predictor-corrector methods, reversing the cycle of 150
Predictor-corrector methods, stability of 143
Preliminary adjustment of a function 25
Proper value see "Eigenvalues (Chapters 8 and 13)"
QD algorithms for transforming power series to and from continued fractions 285
QR algorithms 347
Quadratic convergence 216
Quadratic equations, iterative solution 58
Quadratic factors, evaluation of, from tridiagonal forms 337
Quadratic form of a matrix 209
Quadratic interpolation for table compression 90
Quadrature formulas by the method of undetermined coefficients 108
Quadrature with increasing precision adaptive 105
Quadrature with increasing precision adaptive, Simpson's rule for 104
Quandt 476
Quotient-difference (QD) algorithm 285
Railroad rail problem 3
Rate of convergence of Newton's method 54
Rational function, asymptotic series recast as 263
Rational function, evaluation algorithm 287
Rational function, from continued fraction 286
Ray minimum methods 452
Recurrence methods 11 20
Recurrence relations for  ,  20
Recurrence relations for  23
Recurrence relations for evaluating  21 23
Recurrence relations for Legendre polynomials 434
Recurrence relations, evaluating characteristic polynomials of tridiagonal forms by 332
Recurrence relations, evaluating Fourier series by 11
Recurrence relations, evaluating orthogonal expansions by 11
| Recurrence relations, instabilities in 21
Recursive calculation of finite Fourier series coefficients 231
Recursive evaluation of Fourier series 11
Reduction of banded symmetric matrices 329
Reduction of general matrices to specialized forms 317 340
Reduction to small quantities 60 69 74
Relative error 49
Remes's algorithm 302
Removing a known root in two or more dimensions 370f.
Removing the singularity, need for 121 155 492
Removing two singularities of the form  414 416
Replacement of Laplace's equation on a grid 478f.
Replacing a differential equation on a grid 158 478
Representing a network as a list 503
Representing a network as a neighborhood array 502
Representing a network as a nodal matrix 502
Reversing the predictor-corrector cycle 150
Riccati equation 149
Riccati transformation 149
Richardson extrapolation 106 135
Role of continuity in convergence of Fourier series 226—227
Romberg integration 106
Root suppression 336 370
Root-squaring methods 198
Roots by minimization-a warning 366
Roots near a minimum (maximum) 402
Roots of  387
Roots of a polynomial, shifting 59
Rotational algorithms for eigenvalues Chapter 13
Runge — Kutta 139
Rutishauser 285
Searching for the real roots of a polynomial 184
Secant method 52
Secant method, rate of convergence of 56
Series for tanh x 28
Series from differential equations 15 269
Series replacement of transcendental functions 65 74 424
Series replacement of transcendental functions to reduce variables to small quantities 74
Shifting the eigenvalues of matrices 215
Shifting the eigenvalues of matrices, convergence accelerated by 215
Shifting the root of a polynomial 59
Significant figure loss by subtraction 70
Significant figure loss by subtraction, in alternating series 14 69
Similarity transformation 318
Simpson's rule 102
Simultaneous linear algebraic equations by Cramer's rule 247
Singular integral equation 420
Singular integrals 120
Singularities in an integrand 66 120 412
Singularities, 414
Singularities,  67 123
Singularities, computational 65f.
Singularities, logarithmic 125
Singularities, off-stage 413
Singularities, removable 414 418
Singularities, strength of 67 273
Singularity in an integrand, dividing out 412
Singularity in an integrand, removing 121f. 422f.
Singularity in an integrand, subtracting off 121 123 412
Small quantities, storing 71 498
Smaller root of a quadratic 58
Smallest eigenvalue by shifting 217
Spielberg 284
Square root algorithm 49
Stability, of functional iteration 394 399
Stability, of Milne's method 143
Stability, of Newton's method 50 180
Stability, of recurrence calculations 432
Stability, of the binary chop 179
Stable iterations, construction of 398
Starting an initial-value integration 138
Starting values for functional iterations 47
Statistical data, poor encoding of 250
Stepping searches for polynomial roots 184
Stepping searches for polynomial roots, reduction of by reciprocal transformation 185
Stopping an iteration 48
Strength of a singularity estimated from an integral 267 273
Sturmanian sequence of polynomials 334
Subtracting off the singularity 121 412
Summation orthogonality relations, for finite Fourier series 228
Summation orthogonality relations, for finite orthogonal polynomials 236
Suppressing the unwanted solution in exponential second-order differential equations 170
Suppression of known roots in Newton's method 337
Suppression versus deflation in eigenvalue calculations 336
Symmetric difference in parabolic partial differential equations 445
Symmetry in Fourier series 222
Synthetic division 59 181
Synthetic division, efficient polynomial evaluator 182
Synthetic division, first derivatives from 183
tanh u, continued fraction for 27
Throwback of fourth differences onto second differences 91
Topological ordering by Kahn's algorithm 512
Topological ordering by Klein's algorithm 513
Topological ordering by Knuth's algorithm 513
Topological ordering by Lasser's algorithm 510
Topological ordering of network nodes 509f.
Traffic, Baltimore 503
Trees see "Networks"
Tridiagonal equations 161—162 481
Tridiagonal form, evaluation of characteristic polynomial from 332
Tridiagonal form, LR algorithms for 350
Tridiagonal form, pivoting example 358
Tridiagonal form, QR algorithm for 352
Tridiagonal form, quadratic factors from 337
Tridiagonal form, zeros in 334
Trigonometric approximation see "Fourier series (Chapter 9)"
Trotter 476
Truncation error, in parabolic partial differential equations 445
Truncation error, in quadrature formulas 102 111
Truncation error, in replacements for Laplace's equation 488
Two-point functional iteration 52
Undetermined coefficients, method of 108
Unimportant terms of an equation 58
Unsymmetric matrices, eigenvalues of 220 340
Unvisualizable roots 365
Unwanted solutions in second-order differential equations, suppression of 170
Vector orthogonalization 219
Vibrating masses, eigenproblem for 204
Wasow 483
Wilkinson's pathologic polynomial 201
Work requirements for eigenvalue determinations 353
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