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Young D.M., Gregory R.T. — A Survey of Numerical Mathematics, Volume 2
Young D.M., Gregory R.T. — A Survey of Numerical Mathematics, Volume 2



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Íàçâàíèå: A Survey of Numerical Mathematics, Volume 2

Àâòîðû: Young D.M., Gregory R.T.

ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1973

Êîëè÷åñòâî ñòðàíèö: 673

Äîáàâëåíà â êàòàëîã: 14.07.2014

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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 $(\underline{lim})$      A6
Function of a real variable, limit of a      A5
Function of a real variable, limit superior $(\overline{lim})$      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 $\mathbf{C}^{n}$      719
Inner product in $\mathbf{R}^{n}$      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
1 2 3 4 5 6
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