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| Young D.M., Gregory R.T. — A Survey of Numerical Mathematics, Volume 2 |
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| Ïðåäìåòíûé óêàçàòåëü |
Difference correction method 516 614—624
Difference equation 444 584 951 954—957
Difference equation, solvability 969—970
Difference tables 271—283
Difference tables, central 281
Difference tables, forward 271
Differentiable function of a complex variable A15
Differentiable function of a real variable A9
Differentiable function, numerical differentiation 479
Diffusion equation 951
Digital computer see "Automatic digital computer"
Dimension of a vector space 686
Direct methods 13
Direct methods for linear systems 779—888 1000
Direct power method 227
Directed graph 1002
Directed line segment 676
Dirichlet problem 952
Discrete Dirichlet problem 974
Discrete integrating factor 593—595
Discrete maximum principle 657
Discrete operator 598 605—624
Discriminant 951
Division using a residue number system 849
Divisors of zero 709
Domain A13
Domain of a linear mapping 694
Dominant eigenvalue 915
Dot product 714
Double-length accumulator 43 45
Double-precision arithmetic 42
Douglas — Rachford method 1099
DuFort — Frankel method 1084—1086 1093
Editing subroutines, complex 84
Eigenfunction of a differential operator 658—665
Eigenvalue 172 738
Eigenvalue (characteristic value, proper value, latent root) 738
Eigenvalue (characteristic value, proper value, latent root) for Hermitian matrices 892—914
Eigenvalue (characteristic value, proper value, latent root) for non-Hermitian matrices 914—936
Eigenvalue of a differential operator 577 658—665
Eigenvalue problem for differential equations 658—665
Eigenvalue problem for ordinary differential equations 425 577 658—665
Eigenvalue-eigenvector problems 736—755 889—950
Eigenvalue-eigenvector problems for Hermitian matrices 892—914
Eigenvalue-eigenvector problems for non-Hermitian matrices 914—936
Eigenvalue-eigenvector problems, characteristic polynomial 738 889
Eigenvalue-eigenvector problems, companion matrix 889
Eigenvalue-eigenvector problems, Givens — Householder algorithm 901—914
Eigenvalue-eigenvector problems, Givens' algorithm 899—901
Eigenvalue-eigenvector problems, inverse power method 918—920
Eigenvalue-eigenvector problems, Jacobi's algorithm 893—899
Eigenvalue-eigenvector problems, power method 915—918
Eigenvalue-eigenvector problems, QR algorithm 914 921—936
Eigenvectors, left 944
Eigenvectors, right 944
Element of a matrix 696
Elementary divisor 745
Elementary functions, calculation of 19
Elementary functions, evaluation of 61—66
Elementary functions, exponentials 66
Elementary functions, logarithms 64
Elementary functions, polynomials 62
Elementary functions, square root 61
Elementary rotation matrix 725 893—894
Elementary similarity transformation 924
Elementwise addition of two matrices 698
Elementwise equality of two matrices 697
Elementwise multiplication of a matrix by a scalar 699
Elementwise subtraction of two matrices 700
Elliptic boundary value problem 12 957—958
Elliptic differential equations 957 1000
Elliptic functions 1050
Equilibration 813 814 see
Equivalent systems of equations 791 796 798 802
Error analysis of floating-point operations 46—55
Error analysis, backward (or reversed) 9 46
Error analysis, forward 9
Error squaring method 147
Essential convergence 932
Essentially self-adjoint equation 957—960 990
Euclidean (inner product) space 715
Euclidean (inner product) space, n-dimensional 676
Euclidean length 679 716
Euclidean norm of a matrix 767—768
Euclidean norm of a vector 485 762
Euler method 424 440—449 469 480 486 491 526 1077
Euler method, convergence and accuracy 443—449
Euler method, stability 444
Euler polygon 442
Euler — Cauchy polygon 442
Euler — Maclaurin formula 344—374
Exact difference equation 577 642—647
Exact operators 642—658
Existence theorem for ordinary differential equations 425—431
Experimental observations 12
Exponent, biased 36
Exponent, overflow 44 55 70
Exponent, overflow, testing features 70
Exponent, underflow 45 55 70
Exponent, underflow, testing features 70
Extraneous root 549 567
Extrapolation 1027
Extrapolation, linear 251
Extrapolation, to zero grid size 577 614—615 623—624
Extrema of a function of several variables A17
Field of complex numbers 668
Field of rational numbers 668
Field of real numbers 668
Field, additive identity 667
Field, additive inverse 668
Field, definition 667
Field, multiplicative identity 668
Field, multiplicative inverse 668
Finite dimensional vector space 686
Finite element methods 998
Finite-difference method 953—968
First-order convergence 145
Five-eight rule 365 368
Five-point difference equation 610—614 622—623
Fixed-point arithmetic 16 19
Fixed-point number 32
Fixed-word-length computer 28
Floating-point arithmetic 19 45—55
Floating-point number 32
Floating-point operations, addition 45
Floating-point operations, division 51
Floating-point operations, error analysis of 46—55
Floating-point operations, multiplcation 50
Floating-point operations, rounded 52
Floating-point operations, subtraction 45
Floating-point representations 35—40
Flow diagram 19
FORTRAN 19 56 70
Forward difference formula 350
Forward difference method 1075 1077—1084 1093—1094
Forward difference quotient 442
Forward differences 271
Forward error analysis 9
Fourier series 330—332 952
Fourier series, convergence 330
FRACTION 19
Fraction part of a number 22
Fraction, conversion of representation 24 25
Fraction, rational 20
Fraction, representation of 19
Frobenius (Schur, Euclidean) matrix norm 767—768
Fully indecomposable matrix 816
Function of a real variable A5—A13
Function of a real variable, analytic A11
Function of a real variable, continuous A7
| Function of a real variable, differentiable A9
Function of a real variable, integrable A8
Function of a real variable, limit inferior  A6
Function of a real variable, limit of a A5
Function of a real variable, limit superior  A6
Function of a real variable, piecewise continuous A7
Function of a real variable, power series A12
Function of a real variable, sequence of A11
Function of a real variable, uniformly continuous A7
Function of several variables, relative extrema A17
Function of two real variables, analytic function A14
Function of two real variables, Taylor's theorem A13
Fundamental theorem of algebra 184 244 A19
Fundamental theorem of integral calculus A10
Gauss — Jordan elimination 834 860—880
Gauss — Jordan elimination, using residue arithmetic, more than one modulus 873—880
Gauss — Jordan elimination, using residue arithmetic, single modulus 863—873
Gauss — Seidel method 161 173 1000 1016—1026
Gaussian elimination method 516 587 790—811 970 1000
Gaussian elimination method with iterative improvement 831
Gaussian elimination method, complete pivoting for size 806
Gaussian elimination method, modified 800—811
Gaussian elimination method, partial pivoting for size 806
Gaussian elimination method, triangular decomposition 820
Gaussian elimination method, triangular decomposition with partial pivoting 827
Gaussian elimination method, unmodified 791—799
Gaussian quadrature 345 401—412
Gaussian quadrature, accuracy 409
Gaussian quadrature, coefficients 421
Gaussian quadrature, definiteness 409
General solution 648
General solution of an ordinary differential equation 413
Generalized Dirichlet problem 951 953 968
Generalized eigenvector 753 941 see
Generalized Hermite interpolation 495
Generalized matrix norm 771
Generalized mean-value theorem for integrals 395
Generalized Newton method 161 164—166
Generalized Newton method for polynomials 193—195
Geometric convergence 146
Gerschgorin discs 891
Gerschgorin error analysis 612 666 970—981
Gerschgorin theorems 890—891
Givens — Householder algorithm 901—914
Givens' algorithm 899—901
Globally convergent methods 243—244
Graded nets 996—998
Gradient methods 161 166—171 1069—1072
Graph theory 1002
Graphical methods for a single equation 95 103—105
Greatest lower bound (infimum) A3
Gregory — Newton formula, backward 283
Gregory — Newton interpolation 247 276—280
Gregory — Newton interpolation, formula 365
Group Gauss — Seidel method 1062
Group iterative methods 1062 1064
Group Jacobi method 1062
Group SOR method 1063
Hadamard's inequality 881
Hermite interpolation 247 288—295 344—345 347 495
Hermite interpolation, error of 292
Hermite interpolation, generalized 495
Hermitian conjugate (complex conjugate transpose) of a matrix 719
Hermitian form 733
Hermitian form, nonnegative definite 734
Hermitian form, positive definite 734
Hermitian matrix 720 1001
Hessenberg matrix 923
Heun method 452 470 487 530 1078 1087
Heun method, improved 457—458 472
Heun-midpoint method 457—458 471 487
Higher-order finite difference methods 526 605—641 981—992
Hilbert matrix 324
Hoelder norms 762
Homogeneous linear algebraic equations 737 788
Homogeneous system A18
Homomorphism vector space 677
Householder transformation 901—908
Hyperbolic equation 951
Identity element of a field, additive 667
Identity element of a field, multiplicative 668
Identity element of a vector space, additive 670
Identity mapping 692 713
Identity matrix, additive 700
Identity matrix, multiplicative 708
III-conditioned matrix 324
III-conditioned matrix with respect to the eigenvalue problem 941—949
III-conditioned matrix with respect to the linear equation problem 811
III-conditioned polynomial 889
III-conditioned problem 8 890 941
III-conditioned systems of equations 808
Image (linear transformation) 691
Image space 692 693
Imaginary unit 669
Inconsistent system of equations 780
Indecomposable matrix 816
Infimum (greatest lower bound) A3
Infinite series of matrices 758
Infinite series of matrices, convergence 758
Infinite series of vectors 757
Infinite series of vectors, convergence 757
Infinite series solution of ordinary differential equations 432—435
Initial condition 12
Initial-value problem 12 951 1075—1099
Initial-value problem for ordinary differential equations 423—491 576
Inner product 221 319
Inner product (Euclidean) space 715
Inner product form 733
Inner product in  719
Inner product in  715
Inner product, double-length accumulation of 53
Inner product, floating-point accumulation of 53
INTEGER 23
Integer part of a number 22
Integer, conversion of representation 23 24
Integer, representation of 19 23
Integer, representation of, on a binary computer 28—35
Integrable function A8
Integrable function of a real variable A8
Integral equation formulation for ordinary differential equation 436—441
Integrating factor 589 958
Integrating factor, discrete 593—595
Integration A8
Integration methods to derive difference equations 998
Integration, Romberg 265
Interpolation 11
Interpolation with equal intervals 270—288
Interpolation with trigonometric functions 248 333—340
Interpolation, accuracy 284—286
Interpolation, backward Gregory — Newton 283
Interpolation, bilinear 342
Interpolation, central difference formulas 280—288
Interpolation, Gregory — Newton 247 276—280
Interpolation, Hermite 274 288—295
Interpolation, inverse 247 301—308
Interpolation, Lagrangian 247 258—270
Interpolation, linear 248—258
Interpolation, one variable 247—308 329—340
Interpolation, points 247
Interpolation, smooth 247 295—301
Interpolation, spline 296—301
Interpolation, triangular 340 343
Interpolation, two variables 248 340—343
Intersection of subspaces 681
interval A4
Invariant factor 744
Invariant subspace 748—751
Invariant vector (eigenvector) 737—739
Inverse element in a field, additive 668
Inverse element in a field, multiplicative 668
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