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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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Название: A Survey of Numerical Mathematics, Volume 2

Авторы: Young D.M., Gregory R.T.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 673

Добавлена в каталог: 14.07.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A \delta^{\frac{1}{2}}$-norm      1021 1069
$D^{1 / 2}$-norm      1009
$fl_{2} ()$ arithmetic      53
$L_{2}$-norm      308—318
$L_{p}$-norm      762
Absolute degree of approximation      981 1075 1089
Absolute degree of approximation of a linear discrete operator      606
Acceleration of convergence      95 159—160
Accumulated error      464—468
Accumulator      43
Accuracy of finite difference solutions      597—605
Accuracy of linear multistep methods      493 542—548
Accuracy of methods for solving ordinary differential equations      424
Adams — Moulton method      458—459 488—490 492
Addition of two linear mappings      693
Addition of two matrices      698
Addition of two vectors      672
Addition, modulo m      840
Addition, using a residue number system      846
Adjacent points      953
Adjoint matrix      712
Adjoint matrix, modulo m      856
Aitken $\delta^{2}$ process      159—160
Aitken's method      264—265
Algebra of matrices      702—710
Algebraic compiler language      10
Algebraic eigenproblem      12 736—755 889—950 see
Algol      19
Algorithm, computational      7
Algorithm, computer aspects      5
Algorithm, computer-oriented      2
Algorithm, iteration      14
Algorithm, mathematical aspects      5
Algorithm, stable and unstable      7 9 804 808
Algorithmic language      19
Algorithmic methods      1
Allowable number ranges      71
Allowable numbers      72
Allowable numbers, complex      83
Almost triangular matrix      923
Alternating Direction Implicit method      1000 1039—1062 1075 1096—1097
Alternative discrete representations      590—594
Alternative stability theory      548
Analytic function of a complex variable      A16
Analytic function of a real variable      A11
Analytic function of two variables      A14
Analytic methods for ordinary differential equations      431—435
Analytical solution      1
Approximation      246—248 308—340
Approximation by polynomials      308—317
Approximation by rational functions      248 326—329
Approximation with trigonometric functions      248 333—340
Approximation, best      11
Approximation, continued fraction      328
Approximation, least squares approximation by polynomials      318—325
Approximation, Pade rational approximation      326—329
Approximation, spline      296—301
Approximation, Weierstrass approximation theorem      308
Arithmetic operations, complex      83—91 A14—A15
Arithmetic, $fl_{2}()$      53
Arithmetic, binary      19 21
Arithmetic, complex      83—91 668 A14—A15
Arithmetic, floating-point      45—55
Arithmetic, residue      68 835—888
Arithmetic, rounded floating-point      52
Arithmetic, unnormalized floating-point      68
Arithmetic, variable-precision      68
Assembly language      10
Asymptotic equality      A20
Asymptotic rate of convergence      1015 see
Attainable accuracy      96
Augmented matrix      784
Automatic digital computer      19
Automatic digital computer, characteristics of      19—69
Back-substitution method      794
Backward error analysis      9 46
Backward Euler method      480
Backward Gregory — Newton formula      283
Balancing      950 see
Base (radix), number representation for      19 20
Base for a residue number system      846
Basic derivative      981
Basis      685
Basis ordered      688 695 727
Basis, natural (standard)      689
Bernoulli numbers      375 380
Bernoulli's method      177 222
Bessel's functions      343
Bessel's interpolation formula      281—283
Best approximation      11
Bias of exponent      36 see
Biased characteristic      37
Bilinear form      731
Bilinear interpolation      342
Binary arithmetic      19 21
Binary arithmetic, computer      28
Binary arithmetic, digit (bit)      27
Binary arithmetic, number representation      20
Binary arithmetic, operations      21
Binary arithmetic, point      43
Binary computer      28
Binary digit (bit)      27
Binary number representation      20
Binary operations      21
Binary point      43
Bisection method of      95 105—112
Bit (binary digit)      27
Bit patterns      32
Block diagonal matrix      746 930
Block iteration      1063
Borrowingin binary subtraction      21
Boundary value problems      951—958
Boundary value problems for ordinary differential equations      576—657
CADD      see "Subroutine CADD"
Cancellation      7 see loss
Cancellation law for integers modulo m      840
Cancellation law for scalar multiplication      854
carry bit      44
Carrying in binary addition and multiplication      21
Cauchy bounds      245
Cauchy bounds for roots of polynomial equations      209
Cauchy sequence      A4
Cauchy — Riemann equations      134 164 168 A16 A17
Cauchy's method      142
Cauchy's method for polynomial equations      176
Cauchy's method for polynomials      195—196
CEDIT      see "Subroutine CEDIT"
Central difference interpolation      280—288
Central difference interpolation, Bessel's formula      281—283
Central difference interpolation, Sterling's formula      281—283
Characteristic      37
Characteristic equation for a linear multistep method      549
Characteristic equation for a matrix      738
Characteristic polynomial      738 889
Characteristic value      738 see
Chebyshev polynomial      316 343 1066 1074
Chebyshev quadrature      345 401 412—419
Chebyshev quadrature, abscissas      414
Chebyshev quadrature, definiteness      418
Chebyshev — Gauss quadrature      421
Chinese remainder theorem      874—876
Choi, method of      790
Choleski decomposition      826
Chopping      43
Closed linear multistep method      494
Closed method based on numerical quadrature      453—459
Closed set      A13
Closed-form solution of an equation      95
Closed-form solution of ordinary differential equations      422
CMOD      see "Subroutine CMOD"
Coefficient matrix      784
Coefficients in a linear combination      682
Coefficients of a polynomial      178
Coefficients, Lagrangian interpolation      271
Coefficients, method of undetermined      259—261
Cofactor      711
Cofactor, modulo m      856
Collatz procedure      960
Column of a matrix      696
Column, matrix      716
Column, vector      702
Commutative case      1047—1061
Commutative case, necessary conditions      1060
Commutative case, sufficient conditions      1055—1061
Companion matrix      219 227 889
Comparability theorem for matrix norms      774
Comparability theorem for vector norms      773
Compatible (consistent) norms      761
Complete pivoting for size      806
Complete set of vectors      753
Completely consistent iterative method      121 1064
Complex conjugate      717
complex numbers      668 717
Complex numbers, convergent sequence of      A15
Complex numbers, elementary arithmetic operations      83—91 668 A14—A15
Complex numbers, field of      668
Component of a vector      671 688
Component, natural      689
Componentwise addition of vectors      672
Componentwise convergence      757 774
Componentwise equality of vectors      671
Componentwise multiplication of a vector by a scalar      673
Componentwise subtraction of vectors      678
Composite numerical quadrature formula      371 377
Computational algorithm      7
Computer      see also "Automatic digital computer"
Computer arithmetic      68 see
Computer representable numbers      20 72 96
Computer representable numbers, complex      83
Computer representable numbers, range of      45
Computer, binary      28
Computer, fixed-word-length      28
Computer, negative number representation      29—40
Computer-allowable numbers      72
Computer-allowable numbers, complex      84
Computer-oriented algorithm      2
Concept of a number      22
Condition numbers for the eigenvalue-eigenvector problem      943—950
Condition numbers for the linear equations problem      811
Condition numbers, spectral      811 946—950
Condition of consistency      505 574
Condition of stability      506 574
Conditional stability      493 548—553 567
Conditional transfer      57
Conditional transfer statement      20
Conformable pair of matrices      706
Conformal mapping      952
Congruence for integers      836
Congruence for matrices      851
Conjugate gradient method      1071—1072
Connected component      1006
Connected set      1003
Consistency      1075
Consistency of a linear discrete operator      606
Consistent (compatible) norms      761
Consistent discrete representation      981
Consistent iterative method      121
Consistent linear discrete operator      606
Consistent system of equations      780
Consistently ordered matrix      1023
Constructive methods      1
Continued fraction      328
Continuity      A7 A15
Continuity theorem for matrix norms      774
Continuity theorem for vector norms      772
Continuous function of a complex variable      A15
Continuous function of a real variable      A7
Contraction mapping      125 127
Control data 6600      38
Convergence for iterative methods      1000 1012
Convergence of a sequence of matrices      758
Convergence of a sequence of vectors      756 772
Convergence of a series      A5 A16 757
Convergence of an infinite series of matrices      758
Convergence of an infinite series of vectors      757
Convergence of iterative improvement      832
Convergence of linear multistep methods      493 504—515
Convergence order of, an iterative method      145—159
Convergence order of, Muller's method      154—159
Convergence order of, Newton Method      146—150
Convergence order of, Secant method      150—154
Convergence rates      95
Convergence, acceleration of      159—160
Convergence, componentwise      774
Convergence, criteria for      771—778
Convergence, first order      145
Convergence, geometric      146 159
Convergence, linear      146
Convergence, matrix-norm      774
Convergence, second order      160
Convergence, vector-norm      772 774
Convergent sequence of complex numbers      A15
Convergent sequence of matrices      758
Convergent sequence of real numbers      A4
Convergent sequence of vectors      756 772
Conversion of number representations      22—28
Conversion, binary-to-octal      27 28
Conversion, octal-to-binary      28
Coordinate      676
Coordinate with respect to an ordered basis      696 727—729
Coordinate, mapping      689
Coordinate, vector      688
Corrected Heun method      452 471 487
Corrected value      458
CPOSTED      see "Subroutine CPOSTED"
CQUAD      see "Subroutine CQUAD"
Cramer's rule      2 17 263 787 790 A18
Crank — Nicolson method      1075 1078 1086—1088 1093 1095 1097
Criteria for convergence      771—778
CSQRT      see "Subroutine CSQRT"
Cubic equation      95
Cubic spline function      296—301
Cubic splines      359
Cyclic Chebyshev semi-iterative method      1069
Data space      10
Decimal notation      20
Decomposable matrix      815
Defective matrix      741—743
Deferred approach to the limit      614
Definite formula or method      349 386
Definite methods for numerical quadrature      492
Definiteness, Chebyshev quadrature      416—418
Definiteness, definite formula      349 386
Definiteness, Gaussian quadrature      409
Definiteness, linear interpolation      395—396
Definiteness, Newton — Cotes formulas      392—393 421
Definiteness, Simpson's rule      396—397
Degree of a polynomial      178 A19
Degree of approximation of a linear discrete operator      606
Derogatory matrix      748—751
Descartes' Rule of Signs      197—201 245
Desk calculating machine      2
Determinant evaluation by Chio's method      790
Determinant evaluation by elimination      798
Determinant of a square matrix      711
Determinant of a square matrix, modulo m      855
Diagonal matrix      707
Diagonalizable matrices      742—743 890
Diagonally dominant matrix      826
Diagonally dominant matrix, strictly      298
1 2 3 4 5 6
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