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Golub G.H., Ortega J.M. — Scientific Computing and Differential Equations : An Introduction to Numerical Methods
Golub G.H., Ortega J.M. — Scientific Computing and Differential Equations : An Introduction to Numerical Methods



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Название: Scientific Computing and Differential Equations : An Introduction to Numerical Methods

Авторы: Golub G.H., Ortega J.M.

Аннотация:

Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context.
This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level.


Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 337

Добавлена в каталог: 21.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l_p$ norm      317
Adams — Bashforth methods      45ff
Adams — Moulton methods      47ff 156
Adjoint equation      163
Aho, A.      14
Allgower E.      176 321
Alternating direction method      281
Ames, W.      261 321
Anderson, E.      14 131 231 322
Arioli, M.      131 321
Arrowhead matrix      286ff
Ascher, U.      78 79 149 185 209 321
Asymptotically stable solution      217
Automatic differentiation      174
Axelsson, O.      282 321
B-spline      203$
Back substitution      102ff
Backward differentation formula      64
Backward error analysis      8 115
Backward Euler method      62
Bai, Z.      322
Bailey, D.      110
Bairstow’s method      163
Balancing      117
Ballistics problem      16
Banded matrix      106 118
Bandwidth      106
Barker, V.      282 321
Bartlett, M.      86
Basis functions      179
Becker, E.      282 321
Benzon, W.      14
Bidiagonal matrix      108
Bischof, C      322
Bisection method      150
Block tridiagonal matrix      278
Boundary condition      4 248
Boundary-value problem      67ff
Boundary-value problem, nonlinear      171
Boyle, J.      323
Bramble, J.      77 321
Brenan, K.      36 321
Briggs, W.      305 321
Brown, P.      64 321
Bunch — Kaufman algorithm      141
Bunch, J.      322
Butcher, J.      35 36 53 64 322
Byrne, G.      64 321
Campbell, S.      30 321
Carey, C      282 321 322
Catastrophic cancellation      8
Chain rule      309
Char, B.,      14 322
Characteristic equation      58
Characteristic polynomial      211 314
Cholesky factorization      133 285
Chord method      154
Collocation      180ff 202ff
Companion matrix      163 223
Complete pivoting      119
Composite formulas      197ff
Computational complexity      10
Computational engineering      1
Computational science      1
Computer science      3
Condition number      128ff
Conjugate gradient method      300ff
Conjugate gradient method, preconditioned      301
Conjugate vectors      301
Consistency      53 255 295
Consistently ordered matrix      298
Continuation method      175
Convergence error      9
Convergence factor      159
Convergence theory      154ff 168ff
Convex function      157
Courant, R.      252 322
Crank — Nicolson method      264
Crout form      105
Cubic spline      189ff
Cyclic reduction algorithm      290
Dahlquist, G.      64
Daniel, J.      35 322
Data management      13
Davenport, S.      36 153 326
Davidenko’s method      175
Davis, P.      201 322
deBoor, C.      193 209 322
Deferred correction      77
Deflation      236
Demmel, J.      321 322
Dennis, J.      174 322
Determinant      109 124
Diagonal matrix      316
Diagonally dominant matrix      72 118 120 173 295
Difference equation      57ff
Differential equation      311ff
Differential-algebraic system      36
Diffusion equation      247
Direction vector      300
Dirichlet boundary condition      75 275
Discretization error      8 23ff 70ff 254ff 264
Domain decomposition      286
Dongarra, J.      14 131 231 322 323
Doolittle form      105
DuCroz, J.      322
Duff, I.      14 290 321 322
Edelman, A.      120 322
Efficiency      9
Eigenvalue      211 314
Eigenvalue problem      211
Eigenvalue problem, generalized      216 231
Eigenvalue, ill conditioned      220
Eigenvector      211 314
Eigenvector, computation of      229ff 236ff
EISPACK      11 14 231
Elementary reflection matrix      137
Elliptic equation      247 252
Elliptic norm      317
Elmasri, R.      14 322
Equilibration      116
Erisman, A.      322
Euler equation      185
Euler’s method      22ff 61 199 268
Explicit method      48 253ff
Fast Fourier Transform      290
Fast Poisson solver      290
fill      283
Finite difference method      21 67ff
Finite element method      282
Fischer, C.      14 322
Fix, G.      185 209 282 326
Forsythe. G.      282 323
FORTRAN      12
Forward reduction      102ff
Fourier series      251
Francis, J.      231 323
Friedhoff, R.      14 323
Frobenius matrix      223
Galerkin method      181ff 206ff
Garabedian, P.      252 323
Garbow, B.,      14 231 323
Gauss — Seidel method      292
Gaussian elimination      81ff 101ff 283ff
Gaussian quadrature      200
Gear, C. W.      53 64 323
Geddes, K.      322
Geometric convergence      159
Georg, K.      176 321
George, A      289 323
Gerschgorin’s theorem      217ff
Givens transformation      135
Givens, J.      231
Global convergence      157
Golub, G.      100 110 119 132 141 221 231 244 305
Gonnet, G.      322
Gordon, M.      326
Gould, N.      120 323
Gradient vector      310
Greenbaum, A.      322
Gregory, R.      44 327
Grid points      21 68
Griewank, A.      174 323
Gross, G.      20 326
Haberman, R.      252 323
Hackbrush, W.      305 323
Hageman, L.      303 323
Hager, W.      86 323
Hairer, E.      35 36 324
Hall, C.      186 209 261 282 324
Hammerling, S.      322
Hankel matrix      92
Hanson, R.      100 141 325
Hat function      207
Heat equation      247ff 253ff 273ff 279ff
Hennessy, J.      14 324
Henrici, P.      35 53 63 324
Hessenberg matrix      121 225ff 238
Hestenes, M.      305 324
Heun method      26ff
Higham, N.      110 324
Higher-order differences      77
Hilbert matrix      127
Hilbert, D.      252 322
Hindmarsh, A.      52 64 321 324
Hockney, R.      290 324
Householder reduction      138ff
Householder transformation      137 226
Householder — John theorem      304
Householder, A.      221 231 324
Householder’s method      229
Hubbard, B.      77 321
Hyperbolic equation      247 252 269
IEEE standard      12
Ill-conditioning      8 56 122ff 161
Implicit method      48 262ff
Incomplete Cholesky factorization      302
Initial condition      4 16 248
Inner product      317
Instability      113ff 147ff
Interchanges      112ff
Interpolation      37ff
Interpolation, error      39
Interval of uncertainty      151
Inverse      109
Inverse iteration      236
Irreducible matrix      78
Irreducibly diagonally dominant matrix      79
Isaacson, E.      261 324
Iterative refinement      131
Jacobian matrix      168
Jacobi’s method      230 292
Jesshope, C.      290 324
Jordan elimination      112
Jordan form      214ff 304
Keener, J.      252 324
Keller, H.      79 261 324
Kublanovskaya, V.      231 324
Lagrange polynomials      38
Laguerre’s method      163
Lanczos’ method      241ff
LAPACK      11 14 130 131 231
Laplace’s equation      247
Large sparse matrix      279
Lax equivalence theorem      258
Least squares problems      89ff 139ff
Linear convergence      159
Linear multistep methods      49
Linearly independent eigenvectors      212ff
LINPACK      11 14 130 131
Lotka — Volterra equations      16
LU factorization      103ff 112 285
Macsyma      13
Mai, T.      303 327
Maintainability      11
Maple      13
Mathematica      13
Mathematical model      3
Mathematical model, validation      5
Mathematics      3
MATLAB      11 14
Matrix norm      319
Mattheij, R      321
McKenney, A.      322
Mean value theorem      309 310
Mendez, R.      14 325
Method of lines      271ff
Method of undetermined coefficients      199
Meyer, G.      14 325
Mid-point rule      37 194ff
Milne’s method      64
Minimization      175
Minimum degree algorithm      289
Mixed-type equation      252
Modeling      4
Moler, C      231 322 323 325
Moore, R.      35 322
More, J.      174 322
Morrison, W.      86
Morton, K.      261 265 282 325
Multigrid method      304
Multistep method      45ff 154
Murnaghan — Wintner theorem      215
Natural cubic spline      189
Natural ordering      277
Navathe, S.      14 322
Nested dissection      288
NETLIB      14
Neumann boundary condition      75 275
Newman, W.      14 325
Newton form of interpolation      42
Newton — Cotes formulas      194ff
Newton, R.      20 326
Newton’s method      153ff 168ff 232
Nonlinear equations      145ff l84ff
Nonsingular matrix      315
Norm      128 317
Norm equivalence theorem      319
Normal equations      92
Norsett, S.      35 324
Numerical analysis      2
Numerical integration      193ff
Numerical mathematics      2
Oden, J.      282 321 322
ODEPACK      52
Ohlrich, M.      120 322
One-sided differences      73
One-step method      20ff 27ff 154 295
One-way dissection      288
Operation count      82 105 107 109 136 138
Order of method      28
Ortega, J.      63 79 119 174 176 221 232 290 304 305 325
Orthogonal functions      182
Orthogonal matrix      134ff 318
Orthogonal polynomials      94ff
Orthogonal vectors      318
Ostrowski theorem      298
Ostrowski — Reich theorem      304
Parabolic equation      247 252
Parallel computer      12
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