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| Ïîèñê ïî óêàçàòåëÿì |
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| Young D.M., Gregory R.T. — A Survey of Numerical Mathematics, Volume 2 |
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| Ïðåäìåòíûé óêàçàòåëü |
N-tuple, addition 672
N-tuple, definition 671
N-tuple, equality 672
N-tuple, multiplication by a scalar 673 679
Natural (subordinate) matrix norm 761 769—770
Natural matrix norm 1012
Natural ordering 1023 1068
Negative number representation on a binary computer 35
Negative number representation, ones complement representation 30
Negative number representation, signed absolute value representation 31
Negative number representation, twos complement representation 30
Neighborhood A4 A13 A15
Neighborhood in two dimension A13
Nesting procedure for evaluating polynomials 279
Nesting procedure for polynomials 63
Neumann problem 994
Newton method 14 95 131—136
Newton method for polynomials 176 189—195
Newton method order of convergence 146—150
Newton method, generalized 161 164—169
Newton — Cotes formulas 369—370
Newton — Cotes formulas, closed 370
Newton — Cotes formulas, definiteness 392—393 421
Newton — Cotes formulas, open 370
Nine-point difference equation 984—991 1039
Nonconstructive methods 1
Nondefective matrix 741—743
Nonderogatory matrix 748—751
Nonlinear methods 1069
Nonnegative definite Hermitian form 734
Nonnegative definite matrix 734
Nonnegative matrix 816
Nonnegative real matrix 735
Nonsingular, linear mapping 692
Nonsingular, matrix 298 324 710
Nonsingular, matrix modulo m 855
Nonstationary iterative method 119
Nontrivial solution A19 737
Norm,  308
Norm, , maximum 308
Norm, , of a matrix 9
Norm, , of a vector 9
Norm, , uniform 308
Norm,  (Hoelder) norms 762
Norm, consistent (compatible) 761
Norm, Euclidean norm 762 767—768
Norm, generalized matrix norm 771
Norm, matrix 760
Norm, maximum norm 762
Norm, Schur (Frobenius, Euclidean) norm 767—768
Norm, spectral norm of a matrix 767
Norm, subordinate (natural) matrix norm 761 763
Norm, sum norm 762
Norm, triangle inequality 759 760
Norm, vector 759
Normal derivative boundary conditions 992—995
Normal equations 323
Normal matrix 726 743
Normalized block iteration 1064
Normalized floating-point number 38
Normalized vectors 724
Null (zero) subspace of  680
Null space of a matrix 730 786
Nullity of a linear mapping 694
Nullity of a matrix 730
Number base see "Base"
Number representation 19—23
Number representation, binary 20
Number, conversion of representation 22—28
Number, fraction part 22
Number, integer part 22
Number, representation 22
Numerical analyst 10
Numerical differentiation 11 344—359
Numerical differentiation, accuracy 352—354 385—401
Numerical differentiation, coefficients for 357 420
Numerical differentiation, formulas (table of coefficients) 357 420
Numerical differentiation, two-point 352
Numerical instability 558—574
Numerical instability of algorithms 7 9 803—808
Numerical integration 11
Numerical integration, Romberg 265
Numerical quadrature 11 344—345 361—421 see
Numerical quadrature with singularities 420
Numerical quadrature, accuracy 385—401
Numerical quadrature, coefficients 360—370
Numerical quadrature, composite formula 371 377
Numerical quadrature, equal intervals 361—374
Numerical quadrature, unequal intervals 401—421
Numerical solution 1
Nystrom method 492
o notation A11
Octal (number presentation) 20
One-parameter family of solutions 784
One-parameter family of solutions of ordinary differential equation 423
One-step (single-step) iterative method, stationary 119
One-to-one correspondence 676 689
One-to-one linear mapping 691 692
Ones complement representation 30
Onto (linear transformation) 692
Open linear multistep method 494
Open method, based on numerical, based on numerical quadrature 453—459
Open set A13
Order of a linear multistep method 494
Order of a linear multistep method, limitations 515—525
Order or convergence of a formula 344 346—347
Order or convergence of a method based on numerical differentiation 479
Order or convergence of a method based on numerical quadrature 454—455 461
Order or convergence of an iterative method 145—159
Ordered basis 688 695 727
Ordered basis, coordinates 727—729
Ordinary differential equations 422—492
Ordinary differential equations, accumulated error 464—468
Ordinary differential equations, Adams — Bashford method 492
Ordinary differential equations, Adams — Moulton method 458—459 488—490 492
Ordinary differential equations, analytic methods 431—435
Ordinary differential equations, backward Euler method 480
Ordinary differential equations, closed-form solutions 422
Ordinary differential equations, convergence of numerical methods 424
Ordinary differential equations, eigenvalue problems 425
Ordinary differential equations, Euler method 424 440—449 486 491
Ordinary differential equations, existence and uniqueness theorems 425—431
Ordinary differential equations, first order 422—482
Ordinary differential equations, general solution 423 424
Ordinary differential equations, Heun method 452 487
Ordinary differential equations, Heun method, corrected 452 487
Ordinary differential equations, Heun method, improved 457—458
Ordinary differential equations, Heun method, midpoint 457—458 487
Ordinary differential equations, higher order 422 424 482—483
Ordinary differential equations, infinite series solutions 432—435
Ordinary differential equations, initial-value problem 423—491
Ordinary differential equations, integral equation formulation 436—441
Ordinary differential equations, linear multistep method 482
Ordinary differential equations, method of undetermined coefficients 434—435
Ordinary differential equations, methods based on numerical differentiation 4 478—482
Ordinary differential equations, methods based on numerical quadrature 449—460
Ordinary differential equations, Milne — Simpson method 459 465—468
Ordinary differential equations, modified Euler method 440 450
Ordinary differential equations, Nystrom method 492
Ordinary differential equations, one-parameter family of solutions 423
Ordinary differential equations, open methods 479
Ordinary differential equations, Picard method 424 436—441
Ordinary differential equations, predictor-corrector methods 458—469
Ordinary differential equations, Runge — Kutta methods 473—478 488—490
Ordinary differential equations, self-starting methods 474
Ordinary differential equations, single-step error 461—464
Ordinary differential equations, solution on high-speed computers 488—490
Ordinary differential equations, stability of numerical methods 434
Ordinary differential equations, systems of 422 424 482—488
Ordinary differential equations, systems of first order 482—488
| Ordinary differential equations, Taylor's series method 432—435 487
Ordinary differential equations, two parameter family of solutions 423
Ordinary differential equations, two-point boundary-value problem 424
Orthogonal matrix 724
Orthogonal matrix, improperly 725
Orthogonal matrix, properly 727
Orthogonality 715
Orthonormal set (of vectors) 724
Orthonormal set (of vectors), complete set 753
Overflow (exponent) 45 55 70
Overrelaxation 1027
Pade rational approximation 326—329
Pairwise conjugate vectors 1071
Parabolic equation 951
Partial double precision 490—492
Partial pivoting for size 806
Particular solution 648
Partitioning 1063
Partly decomposable matrix 815
Peaceman — Rachford method 1000 1039—1062 1096—1097 1099
Peaceman — Rachford method, optimum parameters 1050 1062
Peaceman — Rachford method, Peaceman — Rachford parameters 1050—1055
Peaceman — Rachford method, Wachspress parameters 1074
Peano kernel 421
Peano's Theorem 386 393 421
Permutation matrix 726 801 924
Perpendicularity 714
Perron root 816
Perron vector 816
Perron — Frobenius theorem 816
Phenomenon, Runge 296
Physical instability 564
Picard method 424 436—441
Piecewise continuous function of a real variable A7
Pivot for Givens' method 900
Pivot for reduction to Hessenberg form 927
Pivot for the Gaussian elimination method 795
Pivot for the Jacobi method 896
Pivotal equation 795
Pivoting 806
Pivoting, complete 806
Pivoting, partial 806
Plane rotation 725 893—894 900
Poisson integral formula 952
POLLIF see "Subroutine POLLIF"
POLLIN see "Subroutine POLLIN"
Polyalgorithm 177 235—241
POLYHOOK see "Subroutine POLYHOOK"
Polynomial 178
Polynomial equation 176
Polynomial equation, methods for 189—244
Polynomial equation, methods for, Cauchy's 195 196
Polynomial equation, methods for, generalized Newton 193—195
Polynomial equation, methods for, globally convergent 243—244
Polynomial equation, methods for, IP (inverse power) 235—277
Polynomial equation, methods for, Laguerre's 242 244
Polynomial equation, methods for, Lehmer — Schur 197 202—203
Polynomial equation, methods for, Lin 189 192
Polynomial equation, methods for, Lin Bairstow 189 192—195
Polynomial equation, methods for, matrix-related 219
Polynomial equation, methods for, modified Bernoulli 219—227
Polynomial equation, methods for, Muller's 195—196
Polynomial equation, methods for, multiplicity independent 243—244
Polynomial equation, methods for, Newton 189—195
Polynomial equation, methods for, root-squaring 242
Polynomial equation, methods for, secant 189
Polynomial equation, multiple roots of 217
Polynomial equation, quotient-difference algorithm for 242
Polynomial equation, real coefficients, complex roots 217—218
Polynomial equation, resultant procedure for 242
Polynomial equation, roots of 176—245
Polynomial equation, variable-shift procedure for 243
Polynomial evaluation 62
Polynomial, Chebyshev 316 343
Polynomial, coefficients of 178
Polynomial, definition A19
Polynomial, degree of 178 A19
Polynomial, equation 176
Polynomial, Legendre 321 325
Polynomial, multiplicity of a zero 180 A19
Polynomial, nested form of 182
Polynomial, nesting procedure for evaluation 279
Polynomial, reduced 176 179
Polynomial, shift of origin for 187
Polynomial, symmetric function of 185
Polynomial, trigonometric 329
Polynomial, zeros of 176—245 A19
Positional notation for numbers 19
Positive definite Hermitian form 734
Positive definite matrix 324 734 1004
Positive matrix 816
Positive real matrix 735
Power method 221 915—918
Power method with origin shift 917
Power series 62
Power series, convergence A16
Power series, functions of a complex variable A16
Power series, functions of a real variable A12
Power series, radius of convergence A17
Predicted value 457
Predictor corrector methods for ordinary differential equations 458—469
Predictor corrector methods, accuracy of 460—473
Principal vector (generalized eigenvector) 753 941
Procedure A 953 960 970
Procedure B 954 960 974—976
Procedure C 954 960—963 974 976—978 993
Product of a linear transformation by a scalar 693
Product of a matrix by a scalar 699
Product of a vector by a scalar 673 679
Product of two linear mappings 692 703—706
Product of two matrices 706
Program SYMBAL 492
Properly adjacent points 953 1003
Property A 1025
QR algorithm 914 921—936
QR algorithm with origin shifts 932
QR algorithm, the double QR algorithm 934—936
Quadratic equation 77—83 95
Quadratic form 323 732 893
Quadratic form, nonnegative definite 734
Quadratic form, positive definite 734
Quadrature, accuracy 385—401
Quadrature, accuracy formulas 369—370
Quadrature, accuracy formulas, coefficients 369—370
Quadrature, accuracy formulas, Newton — Cotes, closed 370
Quadrature, accuracy formulas, Newton — Cotes, open 370
Quadrature, accuracy, Chebyshev — Gauss 421
Quadrature, accuracy, composite formulas 371 377
Quadrature, accuracy, equal intervals 361—374
Quadrature, accuracy, error 454—459 461
Quadrature, accuracy, Euler — Maclaurin formula 344 374
Quadrature, accuracy, five-eight rule 365 368
Quadrature, accuracy, Gaussian 345 401—412
Quadrature, accuracy, Jacobi — Gauss 421
Quadrature, accuracy, Legendre — Gauss 421
Quadrature, accuracy, mid-point rule 363 368
Quadrature, accuracy, numerical 344—345 361—421
Quadrature, accuracy, rectangle rule 362
Quadrature, accuracy, rectangle rule forward 362 368
Quadrature, accuracy, rectangle rule, backward 362 368
Quadrature, accuracy, Romberg 345 381—385
Quadrature, accuracy, Simpson's rule 365 368
Quadrature, accuracy, Simpson's second rule 369 373
Quadrature, accuracy, trapezoidal rule 363
Quadrature, accuracy, unequal intervals 401—421
Quadrature, accuracy, with singularities 420
Quartic equation 95
Quotient-difference algorithm 178 242
RADD see "Subroutine RADD"
Radius of convergence A12 A17
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