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Johnston R. — Numerical methods, a software approach
Johnston R. — Numerical methods, a software approach

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Название: Numerical methods, a software approach

Автор: Johnston R.

Аннотация:

This book is intended to serve as a text for an introductory course in
numerical methods. It evolved from a set of notes developed for such a course taught to science and engineering students at the University of Toronto.


Язык: en

Рубрика: Математика/Численные методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 276

Добавлена в каталог: 02.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accuracy      19
Adams — Bashforth formulas      248
Adams — Moulton formulas      250
Adaptive quadrature      213 221
Adaptive Romberg quadature      223
Algorithm      18
Aliasing effect      141
ANSI FORTRAN      21
Approximation      119
Approximation by exponentials      128
Approximation by piecewise polynomials      129
Approximation by polynomials      128
Approximation by trigonometric and other forms      129
B-spline      134
B-spline, package      272
Back substitution      31 37
Backward error analysis      49
banking      223
Basis      122
Basis function      122
Basis, local      131
Basis, orthogonal      127 207
beta function      199
Binary search      111
Bisection method      159
Boundary-value problem      236
Bracket      159
Brent’s method      172
Broyden’s method      189
Cancellation      12
Cautious Romberg integration      220
Characteristic polynomial      64
Cholesky factorization      58
Chopping      7
Column convergence      220
Communications vector      261
Condition number      50 84 184
Convergence      150
Cramer’s Rule      87 149
Definite integral      199
Deflation      151 174 182
Diameter      152 157
Difference equation      16 17
Differential equation      17 233
Differential equation, general solution      233
Differential equation, numerical solution      16 238
Differential equation, particular solution      234
Differential equation, series solution      235
DIMENSION      122
Divided difference      103 168 203
Divided difference, and derivative      104
Divided difference, table      102
Documentation      20
doubly linked list      60
Dynamic allocation      41
ease of use      20
Eigenvalue      26 64
Eigenvalue, dominant      74
Eigenvector      26 38 74
EISPACK package      271
Elimination      31 37
Elimination in place      34
Elliptic integral      232
EPS      8
Equivalent problem      27
error control      3
Error vector      46
Error, absolute      4 154
Error, global      240
Error, growth      48
Error, in approximation      123 135
Error, in interpolation      104
Error, inherent      3
Error, local      241
Error, propagation      29 242
Error, quadrature      203
Error, relative      4 7 46 154
Error, round-off      3 7
Error, tolerance      54
Error, truncation      3
Euler’s formula for $e^{ix}$      138
Euler’s formula for differential equations      239
EXPONENT      5
F-test      156
Fast fourier transform, (FFT)      142
Fehlberg’s method      247
Fill-in      60
Finite difference Newton method      188
fixed-point      150
Fixed-point iteration      150 169 259
Fixed-point number system      4
Floating-point number system      4
FLOP      9
Fourier coefficient      139
Fourier series      129 139
Fractional part      5
Function space      119 120 207
Gamma function      199 211
Gauss elimination and back substitution      28 31 149
Gauss elimination and back substitution, algorithm      37
Gauss quadrature      206 226
Gauss quadrature, points      208
Gauss quadrature, rules      206
Gauss — Jordan method      87
Generating set      120
Global convergence      152 180
Goodness of fit      95
Guard digit      9
Hermite polynomials      211
Hessenberg matrix      71
Hexadecimal number system      23
Hybrid method      168 172
Ill-conditioned      49 155 183 257
Improper integral      224
IMSL package      270
Initial condition      16 236
Initial-value problem      236
Instability      16
Interpolation      96
Interpolation, by cubic splines      114
Interpolation, by piecewise cubic Hermite      113
Interpolation, by piecewise linear      109
Interpolation, conditions      96
Interpolation, osculatory      106 113
Interpolation, piecewise polynomial      109 205
Interpolation, polynomial      97 201
Inverse iteration      38 74
Inverse quadratic method      171 172
Iteration      150
Iterative improvement      16 38 51
Iterative method      150
Jacobian matrix      185 257
Joints      109
K-step formula      248 252
Knots      109
Knots, variable      137
Kronecker delta      202
Laguerre polynomials      211
Laguerre’s method      179
Least-square, approximation      124
Least-square, solution      77
Length-preserving      70
linear combination      120 121
Linear dependence      122
Linear equations      26 28
Linear equations, overdetermined      26 76
Linear independence      121
LINPACK package      271
Lobatto rules      228
Local problem      241
Local solution      242
LU decomposition      28 31
Machine epsilon      8 21
Machine hardware precision      54
Mathematical model      95
Mathematical software      1
MATLAB package      272
Matrix, band      59 132 135
Matrix, companion      194
Matrix, conjugate transpose      140
Matrix, defective      64
Matrix, determinant      32 33
Matrix, eigenvalue      64
Matrix, eigenvector      74
Matrix, Hessenberg form      71
Matrix, orthogonal      66
Matrix, permutation      31
Matrix, positive definite      58
Matrix, quasi-triangular      65
Matrix, rank      79
Matrix, similar      66
Matrix, singular value      82
Matrix, sparse      60 187
Matrix, symmetric      57
Matrix, tridiagonal      73
Matrix, unit triangular      28 36
Matrix, unitary      140
Matrix, Vandermonde      99
Matrix-vector notation      28
Mean-value theorem for derivatives      105
Mean-value theorem for integrals      203
method      18
Minimal degree algorithm      61
Minmax solution      77
MINPACK package      272
Modified Gram — Schmidt (MGS)      80 127
Muller’s method      171
Multiplier      29
Multistep formulas      248
NAG package      271
NDIM      40
Neighborhood      152 157
Newton — Cotes ruler      202
Newton — Raphson method      151 168 260
Newton’s method      185
Nonlinear equation      148
Norm, $l_1$      77
Norm, $l_2$      45
Norm, $l_p$      45
Norm, of matrix      46
Norm, of vector      45
Norm, uniform      77
Normal equations      79
Numerical singularity      40 55
One-step, two-half steps      214 222 241 250
Operations count      22
Order of accuracy      243
Orthogonal      49
Orthogonal basis      127 207
Orthogonal functions      140 206 209
Orthogonal matrix      66
Overdetermined linear system      26 76 124
Overflow      6
Packed form      57 59
Period      138
Periodic function      138
Piecewise polynomial      109
Piecewise polynomial, cubic Hermite      113
Piecewise polynomial, cubic spline      114
Piecewise polynomial, linear      109
Piecewise polynomial, quadratic      113
Pivot element      29
Pivot vector      32
Pivotting, complete      31
Pivotting, partial      31
Pivotting, strategy      32 60
Polynomial      177
Polynomial, Hermite      211
Polynomial, Lagrange form      99 120 201
Polynomial, Laguerre      211
Polynomial, Legendre      144 211
Polynomial, nested form      97 102 177
Polynomial, Newton form      101 201
Polynomial, Tchebychev      211
Polynomial, trigonometric      138
Portability      20
Power method      74 92
Predictor-corrector pair      251
Premature termination      154
Preprocessing      62
Prime factorization      142
Propagation effect      256
Pseudo inverse      83
QR, algorithm      64 69 84
QR, factorization      67 80
QR, transformation      69
QUADPACK package      272
Quadratic equation      11 149
Quadrature      199
Quadrature, adaptive      221
Quadrature, adaptive Romberg      223
Quadrature, algorithm      212
Quadrature, composite rules      205
Quadrature, error      203 209 213
Quadrature, Gauss rules      206
Quadrature, Newton — Cotes rules      202
Quadrature, points      200
Quadrature, Romberg      214
Quadrature, rule      199
Quasi-Newton methods      188 260
Rank-one update method      191
Rate of convergence      158
Real valued function      159
RECURSIVE      223
Regula falsi method      162 165
Relative correction      54
Relative density      4
Relative separation      184
Reliability      19
Removable singularity      225
Residual      45 123 124
Residual, relative      47
Robustness      19
Romberg integration      214
Romberg table      214
Roof function      130
Root      149
Root mean square error      79 135
Rounding      7
Row convergence      217
Runge — Kutta formulas      243
Scalar function      186
Secant line      163 166
Secant method      165 168 188 260
Semilog fit      128
Separation      184
Shape preserving      70
Shooting method      266
Similarity transformation      66
Simpson’s rule      203 206
Singular value decomposition (SVD)      82
Sparse matrix algorithm      60
Spectral radius      91
Spline, basis form      131
Spline, clamped boundary      115
Spline, cubic      114 133
Spline, free boundary      115
Spline, linear      113 130
Spline, piecewise form      131
Spline-on-spline      145
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