Shampine L.F., Allen R.C., Pruess Jr.S. — Fundamentals of numerical computing :: Электронная библиотека попечительского совета мехмата МГУ

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Shampine L.F., Allen R.C., Pruess Jr.S. — Fundamentals of numerical computing

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Название: Fundamentals of numerical computing

Авторы: Shampine L.F., Allen R.C., Pruess Jr.S.

Аннотация:

This book examines the solution of some of the most common problems of numerical computation. By concentrating on one effective algorithm for each basic task, it develops the fundamental theory in a brief, elementary way. There are ample exercises, and codes are provided to reduce the time otherwise required for programming and debugging. Exposes readers to art of numerical computing as well as the science. Readers need only a familiarity with either FORTRAN or C. Applications are taken from a variety of disciplines including engineering, physics, and chemistry.

Язык:

Рубрика: Математика/Численные методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 268

Добавлена в каталог: 01.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Absolute error      1
Accuracy of linear system algorithms      48—61
Accuracy of polynomial interpolation      98—101
Accuracy of quadrature      184—187
Accuracy of spline interpolation      111—113
Adams methods      240—243
Adams — Bashforth formula      241
Adams — Moulton formula      242
Adapt (code)      188—189
Adaptive quadrature      184—188
AVINT      201
Back substitution      35
Backward differentiation formulas      243
Backward error analysis      49
Band matrix      65
Base of a number system      9
Bilinear polynomial      122—123
Binary search      138
Bisection method      138
Bracket      138
breakpoints      101
C (language)      vi
C++      vi
Cancellation error      16
Chebyshev interpolating points      88
Chopped arithmetic      7
Composite trapezoid rule      181
Condition number      56
Condition number inequality      57
Conditioning      1
Conditioning of a linear system      55—61
Conditioning of a nonlinear equation      158
Cubic spline      103—115
Curve drawing      130—131
Dawson's integral      190 212 217—218
Degree of precision      172
Determinant      6 62 81
Diagonally dominant matrix      65
Differential equations      210—215
Divided difference table      95—96
Divided differences      93—98
Elimination      see Gaussian elimination
End conditions      108
England      see Runge — Kutta — England method
Error estimation in Adapt      184—187
Error estimation in Rke      230—235
Error in polynomial interpolation      88—93 98—101
Error in spline interpolation      102—103 112
Euler — Maclaurin formula      181
Euler's method      217
Extrapolation      183
Factor (rode)      61
Filon quadrature      26 128—130
Floating point distribution      10—11
Floating point notation, fl(x)      7
Floating point number system      9
Floating point representation      9
Fortran 77      vi
Fortran 90      vi
Fundamental theorem of integral calculus      253
Galerkin' s method      72 170
Gamma function      13—14
GAMS      vii
Gauss — Seidel method      76
Gaussian elimination      32—42
Gaussian quadrature      177
Global error (for ODE's)      228
Hetm's method      225
Higher order systems of differential equations      214—215
IEEE arithmetic      10
Ill-conditioned      2
Initial value problem      210—211
Integration by parts      253
Intermediate Value Theorem      252
Interpolation error      85—93 98—101 102—103 112
Interpolation in the plane      119—127
Interpolation polynomial      82—101
Interpolation, cubic spline      106—113
Interpolation, inverse      148
Interpolation, shape preserving spline      104—106
Inverse matrix      31 63
Iterative refinement      55
Jacobi iteration      76
Knots      101
Lagrange form      83
LAPACK      66 70
Linear system      30
LINPACK      66 70
Lipschitz condition      211
Lipschitz constant      211
Local error      222 228—231 233—235
Loss of significance      16
Lotka — Volterra equation      163
Lower triangular matrix      44
LU factorization      44—48
Maclaurin series      253—254

Mantissa      4
Mathcad      136 147 155 183 244 248
Mathematica      vi 244
MATLAB      vi 27 150 151 157 244
Matrix      30
Mean Value Theorems      252
Midpoint rule      178
Minimum curvature property      111
Modification of right-hand-side      40
Muller's method      147
Multiple root      134
Multistep method      240—244
Natural cubic spline      110 112
Natural end condition      110
NETLIB      vii
Newton divided difference form      95
Newton — Cotes formulas      174
Newton's method for a single equation      140
Newton's method for systems      160—162
nodes      83
Nonlinear equations, scalar      134—160
Nonlinear equations, systems of      160—162
Nonsingular matrix      30
Normalized floating point number      4 9
Norms      53
Numerical integration      see Quadrature
One-step methods      221—223
Order      221
Oscillatory integrand      192
Overflow      5
Partial pivoting      39
Periodic end conditions      108
Periodic integrand      181—182 192—193
Piecewise polynomial      101
Pivot      35
Poisson's equation      72
Pole      136
Polynomial interpolation      83—98
Positive definite matrix      65
QUADPACK      184 186—187
Quadratic convergence      141
Quadratic equation      17
Quadrature formula      172
Relative error      1
Residual of a linear system      22 51
Residual of a nonlinear equation      136
Right-hand-side vector      30
Rke (code)      236—238
RKSUITE      244
Rolle' s theorem      252
Romberg integration      183
Root      134
Root of a nonlinear system      160
Root of a quadratic      17
Rootof a single function      134
Rounded arithmetic      7
Runge — Kutta formulas      224—227
Runge — Kutta, classical      226
Runge — Kutta, England method      231—233
Runge's function      91 93
Secant method      140
Simple root      134
Simpson's rule      177
Singular integrand      193—198
Singular matrix      30
Solve (code)      62
SPLINE      101
Spline, complete cubic      110 200
Spline, shape preserving      104—106 200—201
Spline-coeff (code)      113—115
Spline-value (code)      113—115
Stability      2
Stiff diffferential equation      243
Stirling's approximation      14 206—207
Symmetric matrix      70
Systems of differential equations      212—214
Systems of linear equations      30—31
Systems of nonlinear equations      160—162
Tabular data, integration of      200—201
Taylor series      223 252
Taylor's theorems      252—253
Trapezoid Rule      176
Triangular matrix      35
Tridiagonal matrix      68
Underflow      5
Undetermined coefficients      175
Unit roundoff      9
Unstable      2
Upper triangular matrix      35
Weight function      171—173
Weight quadrature      171
Well-conditioned      1
Wilkinson polynomial      158—159
Yvalue (code)      236—238
Zero      see Root
Zero (code)      152—155

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