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| Young D.M., Gregory R.T. — A Survey of Numerical Mathematics, Volume 2 |
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| Предметный указатель |
Inverse element in a vector space, additive 670
Inverse interpolation 247 301—308
Inverse interpolation, accuracy 303—307
Inverse interpolation, linear 302
Inverse interpolation, using Muller's method 302
Inverse interpolation, using the IP (inverse power) method 302
Inverse interpolation, using the method of false position 302
Inverse interpolation, using the secant method 302
Inverse linear interpolation 302 343
Inverse mapping 692 713
Inverse power method 227 245 918—920
Inverse quadratic interpolation 343
Inverse, additive, in a field 668
Inverse, additive, of a matrix 700
Inverse, multiplicative, in a field 668
Inverse, multiplicative, of a matrix 710—713 779
Inverse, multiplicative, of a matrix modulo m 855—857
Inverse, multiplicative, of an integer modulo m 840—843
Inverse, multiplicative, using a residue number system 847
IP method (inverse power) 177 227 235
IP method (inverse power) for inverse interpolation 302
Irreducible matrix 1001
Irregular boundaries 960—963 see B and
Irregular points 954
Isomorphism, vector space 677 689
Iteration function 140
Iteration-algorithm 14
Iterative improvement 831—832
Iterative method for finding linear discrete operators 637—642
Iterative methods 13
Iterative methods for linear systems 999—1074
Iterative methods for the solution of equations 95 105—160
Iterative methods order of convergence 145—159
Iterative methods, completely consistent 121
Iterative methods, consistent 121
Iterative methods, generation of 127—131
Iterative methods, nonstationary 119
Iterative methods, reciprocally consistent 121
Iterative methods, stationary 119
JACOBI algorithm 893—899
Jacobi algorithm, ordinary cyclic 896
Jacobi algorithm, special cyclic 896
Jacobi algorithm, threshold 896
Jacobi method 161 172—173 1000 1007—1016 1095 1098
Jacobi — Gauss quadrature 421
Jacobian 164 963
JOR method 1098—1099
Jordan canonical form 743 776
Kernel of a linear mapping 694
Kernel, dimension 694
Kronecker delta 682
Kutta's third-order rule 476
l'Hospital's rule 133 A10
L-matrix 1001
Lagrangian interpolation 247 258—270 344—345
Lagrangian interpolation, coefficients 271
Lagrangian interpolation, convergence and accuracy 266—270
Laguerre's method 178 242 244
Laplace's equation 12 951—952 995
Least squares, approximation by polynomials 318—325
Least squares, approximation by polynomials, problem 12
Least squares, approximation by polynomials, trigonometric approximation 338—340
Least upper bound (supremum) A3
Left eigenvectors 944
Legendre polynomials 321 325 402—408
Legendre — Gauss quadrature 421
Lehmer — Schur method 197 202—203
Levelled reference-polynomial 310
LIMIT A5
Limit inferior  A6
Limit inferior , function of a real variable A6
Limit of a function A5
Limit of a function of a real variable A5
Limit of a sequence A4
Limit superior  A6
Limit superior , function of a real variable A6
Limit, point A13
Limiting characteristic equation for a linear multistep method 549
Lin — Barstow method 176 189 192—195
Lin's method 176 189 192
Line Gauss — Seidel method 1063
Line iteration 1063
Line Jacobi method 1063
Line SOR method 1063
Linear algebra A18
Linear algebraic equations 8 779 A18
Linear algebraic equations, augmented matrix 784
Linear algebraic equations, back substitution method 794
Linear algebraic equations, coefficient matrix 784
Linear algebraic equations, computational methods for solving 790—833
Linear algebraic equations, condition numbers 811
Linear algebraic equations, consistent system 780
Linear algebraic equations, equivalent systems 791 796 798
Linear algebraic equations, exact solution 835
Linear algebraic equations, Gauss — Jordan elimination 860—880
Linear algebraic equations, Gauss — Jordan elimination, using residue arithmetic, more than one modulus 873—880
Linear algebraic equations, Gauss — Jordan elimination, using residue arithmetic, single modulus 863—873
Linear algebraic equations, Gaussian elimination 790—811
Linear algebraic equations, homogeneous system 788 A18
Linear algebraic equations, ill-conditioned systems 808
Linear algebraic equations, inconsistent system 780
Linear algebraic equations, iterative improvement 831
Linear algebraic equations, method of iterative improvement 807 831
Linear algebraic equations, residue arithmetic 835—888
Linear algebraic equations, solution 779
Linear algebraic equations, triangular decomposition 820
Linear algebraic equations, triangular decomposition, with partial pivoting 827
Linear combination of vectors 682
Linear combination, coefficients 682
Linear combination, nontrivial 682
Linear combination, trivial 682
Linear convergence 146
Linear discrete operator 605—624
Linear discrete operator, exact 642—658
Linear extrapolation 251
Linear interpolation 96 248—258
Linear interpolation in three variables 163
Linear interpolation, convergence and accuracy 251—258
Linear interpolation, definiteness 395—396
Linear mapping see "Linear transformation"
Linear multistep method 482 493—558
Linear N-step method see also "Linear multistep method"
Linear N-step method, maximum order method 498
Linear stationary iterative method 1069
Linear transformation 667 690—693
Linear transformation, domain 694
Linear transformation, identity 692
Linear transformation, image space 692
Linear transformation, kernel 694
Linear transformation, matrix 696
Linear transformation, nonsingular 692
Linear transformation, nullity 694
Linear transformation, onto 692
Linear transformation, product by a scalar 693
Linear transformation, range 694
Linear transformation, rank 694
Linearly dependent, set of vectors 683
Linearly dependent, set of vectors, on the vectors 684
Linearly independent functions 642—643
Linearly independent set of vectors 683
Lipschitz condition 123 425 436—437 442 486 494 577 580
Local truncation error 492
Localization theorems 890—891
Logarithms 64—66
Logical flow diagram see "Flow diagram"
LR-algorithm 921
LU-Decomposition 820
M-matrix 1021
Machine C 38 73 99
Machine D 55
| Machine languages 10
Machine-representable numbers 7 see
Majorant function 599 604
Mantissa 37
Mathematical induction A19
Mathematical instability 558—574
Mathematical model 423
Matrix of a Hermitian form 733
Matrix of a quadratic form 732
Matrix of an inner product form 733
Matrix, additive inverse 700
Matrix, adjoint 712
Matrix, augmented 784
Matrix, block diagonal 746
Matrix, Choleski decomposition 826
Matrix, conformable pair 706
Matrix, decomposable 815
Matrix, defective 741
Matrix, derogatory 748—751
Matrix, determinant of 711
Matrix, diagonal 707
Matrix, diagonalizable 742—743 890
Matrix, diagonally dominant 826
Matrix, eigenvalue (characteristic value, proper value, latent root) 738
Matrix, eigenvector (characteristic vector, proper vector, latent vector) 739
Matrix, elementary rotation 725 893—894
Matrix, equality 697
Matrix, equilibrated 814
Matrix, fully indecomposable 816
Matrix, hermitian 720
Matrix, Hermitian conjugate 719
Matrix, identity 708
Matrix, identity, additive 700
Matrix, identity, multiplicative 708
Matrix, indecomposable 816
Matrix, invariant subspace 748—751
Matrix, inverse, additive 790
Matrix, inverse, multiplicative 710—713
Matrix, Jordan canonical form 743—752
Matrix, modal 740
Matrix, nondefective 741
Matrix, nonderogatory 748—751
Matrix, nonnegative 816
Matrix, nonnegative definite 734
Matrix, nonnegative real 735
Matrix, nonsingular 710
Matrix, normal 726 743
Matrix, null space of a 730
Matrix, nullity of a 730
Matrix, orthogonal 724
Matrix, over the complex field 697
Matrix, over the real field 697
Matrix, partly decomposable 815
Matrix, permutation 726 801
Matrix, plane rotation 725 893—894
Matrix, positive 816
Matrix, positive definite 734
Matrix, positive real 735
Matrix, principal vector 753
Matrix, rank 730
Matrix, residue 852
Matrix, row rank 730
Matrix, row space 730
Matrix, scalar 707
Matrix, singular value 755
Matrix, skew-symmetric 892
Matrix, spectral radius 739—767
Matrix, square root 755
Matrix, symmetric 720
Matrix, transpose 712
Matrix, tridiagonal 901 909
Matrix, unitary 724
Matrix, unitary similarity transformation 754
Matrix, zero (null) 700
Matrix-norm convergence 774
Maximum norm 308 488 762 see
Maximum of a set of real numbers A3
Mean-value theorem A8
Mean-value theorem for integrals A8
Mesh points 583
Mesh ratio 1077—1078
Mesh size 584
Method of bisection 95 105—112 578
Method of false position 95 112—118 578
Method of false position for inverse interpolation 302
Method of finite differences for eigenvalue problems 662—665
Method of finite differences for two-point boundary value problems 576 583—657
Method of steepest descent 1070
Method of superposition 576 579—583
Method of superposition for eigenvalue problems 658—662
Method of undetermined coefficients 259—261
Method of undetermined coefficients for Hermite interpolation 289
Method of undetermined coefficients for ordinary differential equations 434—435
Method of undetermined weights 262—264 344—350
Method of undetermined weights for Hermite interpolation 289
Methods based on numerical differentiation 478—482
Methods based on numerical differentiation, open methods 479
Methods based on numerical quadrature for ordinary differential equations 449—460
Metric space 127
Midpoint method 453 480 531 1077 1085
Midpoint rule 362 368
Milne — Simpson method 459 465—468
Minimum of a set of real numbers A3
Minimum principle for three-point operators 653—656
Minus zero 29 32
Mixed derivative 954
Mixed derivative, elimination 963—968
Mixed type 951
Modal, equation 740
Modal, matrix 740
Model problem 1014 1023 1035 1051 1064
Modified Bernoulli method 219—227
Modified Euler method 440 450 526 1078 1087
Modified Heun method 1078 1087
Modified SOR method with fixed parameters 1068—1069
Modified SOR method with variable parameters 1068—1069
Modulus 836
Modulus of a complex number A14
MSOR method see "Modified SOR method"
Muller's method 95 136—145 578 659
Muller's method for inverse interpolation 302
Muller's method for polynomial equations 176
Muller's method for polynomials 195—196
Muller's method order of convergence 154—159
Multiplication of a linear mapping by a scalar 693
Multiplication of a matrix by a scalar 699
Multiplication of a vector by a scalar 673 679
Multiplication of two linear mappings 692 703—706
Multiplication of two matrices 706
Multiplication, modulo m 840
Multiplication, using a residue number system 847
Multiplicative identity (matrices) 708
Multiplicative identity (matrices), left identity 708
Multiplicative identity (matrices), right identity 708
Multiplicative inverse in a field 668
Multiplicative inverse of a matrix 710—713 779
Multiplicative inverse of an integer modulo m 840—843
Multiplicity independent methods 243—244
Multiplicity independent methods for polynomial equations 178
Multiplicity of a zero 94 A19
Multiplicity of a zero of a polynomial 180
Multiplicity of a zero of an arbitrary function 93 94
Multiplicity of an eigenvalues 747
Multiplicity of an eigenvalues, algebraic 752 941
Multiplicity of an eigenvalues, geometric 752 941
Mutually orthogonal vectors 724
n-dimensional coordinate space, complex  672
n-dimensional coordinate space, real  671 676
n-dimensional coordinate vector 676
n-dimensional coordinate vector, definition 671
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