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Higham N. — Accuracy and stability of numerical algorithms
Higham N. — Accuracy and stability of numerical algorithms



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Название: Accuracy and stability of numerical algorithms

Автор: Higham N.

Аннотация:

Treats the behavior of numerical algorithms in finite precision arithmetic, combining algorithmic derivations, perturbation theory, and rounding error analysis and emphasizing software practicalities, with particular reference to LAPACK and MATLAB. Includes historical perspectives, especially on the work of Wilkinson and Turing, with quotations introducing chapters on subjects such as floating point summation, condition number estimation, and the Sylvester equation. Although designed as a reference rather than a text, it includes problems and solutions. Annotation c. by Book News, Inc., Portland, Or.


Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 688

Добавлена в каталог: 23.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Lyapunov equation, discrete-time      322
Lynch, Robert E.      32
Lyness, J. N.      32 441
Lynn, M. Stuart      327
M-matrix      580
M-matrix, stability of LU factorization      198
M-matrix, triangular      157 159 160
Mac Lane, Saunders      483
Machar code      497—498
Machine epsilon      41
Macleod, Allan J.      197
Magic square matrix, p norm of      127
Makhoul, John      225
Malcolm, Michael A.      33 95 97 196 245q 262 305 497 509 525
Manteuffel, Thomas A.      165
Mantissa      40
Maple      6 181 506
Marine, F.      461
Markov chain, perturbation analysis for      146
Marovich, Scott B.      576
Marsaglia, George      527
Martin, R, S.      196
Mascarenhas, Walter      197
Mathematical      6 181 506
Mathias, Roy      165 223 386 515
MATLAB      3 43 583
MATLAB, condest      304 480
MATLAB, fft      468
MATLAB, inv      271
MATLAB, rand      518
MATLAB, randn      518
MATLAB, rcond      305 480 489
MATLAB, roots      483
MATLAB, special matrices      514
MATLAB, Symbolic Math Toolbox      3 521
MATLAB, Test Matrix Toolbox      591—594
Matrix multiplication, backward error      85
Matrix multiplication, error analysis      76—78 85
Matrix multiplication, fast methods      445—463
Matrix norm      see “Norm”
Matrix, block diagonally dominant      251
Matrix, Cauchy      516—517
Matrix, circulant      468
Matrix, companion      525—526
Matrix, comparison      157
Matrix, condition number      121—123 126 392
Matrix, confluent Vandermonde-like      429
Matrix, convergent      348
Matrix, diagonally dominant      181
Matrix, distance to singularity      123 140
Matrix, Drazin inverse      336—337
Matrix, Fourier      179
Matrix, Hadamard      128 179 181 201
Matrix, Hilbert      514—517
Matrix, inversion      261—287 (see also “Inverse matrix”)
Matrix, involuntary      521
Matrix, Kahan      161 167 214
Matrix, M-matrix      580
Matrix, magic square      127
Matrix, moment      520
Matrix, nonsymmetric positive definite      223
Matrix, Pascal      520—524
Matrix, powers of      345—359 (see also “Powers of a matrix”)
Matrix, pseudo-inverse      392 409 412 416
Matrix, random      517—520
Matrix, randsvd      519—520
Matrix, second difference      525
Matrix, semiconvergent      337
Matrix, Sylvester’s introduction of term      309
Matrix, symmetric indefinite      218
Matrix, symmetric positive definite      204
Matrix, symmetric positive semidefinite      210
Matrix, symmetric quasidefinite      229
Matrix, test      513—528
Matrix, totally nonnegative      176
Matrix, tridiagonal      183—186
Matrix, tridiagonal, Toeplitz      524—525
Matrix, Vandermonde      426
Matrix, Vandermonde-like      429
Matrix, vet-permutation      319 323
Matsui, Shouichi      53
Mattheij, R. M. M.      257
Matula, David W.      54 57 62
Mazzia, Francesca      197
McCarthy, Charles      146
McCracken, Daniel D.      83 100 113
McKeeman, William Marshall      196 241
McKenney, Alan      322 527
Meaningless answers, why you might get them      35
Meinguet, Jean      224 284
Mendelssohn, N. S.      286
Metcalf, Michael      3
Metropolis, N.      489
Meurant, Gerard      257 305
Meyer, Jr., Carl D.      147 337
Miiller, K. H.      113
Milenkovic, Victor J.      34
Miller, D. R.      322
Miller, Webb      83 115 451 454 473q 487 488 507 517 576
Miranker, Willard L.      486
Mirsky, L.      558
Misconceptions, of floating point arithmetic      31
Mixed forward-backward error      8
Modified Gram — Schmidt method      see “Gram — Schmidt method modified”
Moler, Cleve B.      33 34 59 84 95 164 190 196 197 231q 235 241 243 245q 261q 262 282 297 304 305 323 345q 348 359 391q 415q 441 503 508 511 526 579q
Moller, Ole      92
Moment matrix      520
Monotone norm      119
Montgomery, D.      186
Moore — Penrose conditions      412
Moore, Ramon E.      486
Morrison, Donald      503 511 579
Morton, K. W.      32
Most significant digit      40
Mukherjea, Kalyan      382
Muller-Merbach, H.      32
Multi-directional search method      477—479
Multiple precision arithmetic      504—506
Multiple precision arithmetic, Bailey’s package MPFUN      505
Multiple precision arithmetic, Brent’s package      486 504
Murakami, H.      483n
Murray, Walter      32 225 226 422 479
Mutation testing      517
NAG Library      583—584
NAG Library, LAPACK in      588
NAG Library, machine constants      500
Nagy, James G.      471
Nan (not a number)      46 492 495
Nash, Stephen G.      312 324 391q 567
Nashed, M. Zuhair      409
Nelder — Mead simplex method      479
NETLIB      582—583
Neumaier, A.      61 94
Neumann, M.      198
Newbery, A. C. R      113
Newcomb, Simon      51
Newman, Morris      514 520
Nickel, Karl      94 486
Nilson, E. N.      167
Nonlinear equations, references for rounding error analysis      32
Nonsymmetric positive definite matrix      223
Nonsymmetric positive definite matrix, LU factorization, stability of      223—224
Nordio, Marcelo      197
Norm      117—129
Norm equivalence constants      122t
Norm, $\|\cdot\|_{\alpha,\beta}$ explicit formulae for      128
Norm, 2-norm, evaluation without overflow      502—503
Norm, absolute      119
Norm, consistent      120
Norm, dual      119
Norm, Frobenius      120
Norm, Holder inequality      118
Norm, matrix      120—124
Norm, matrix p-norm      124—126
Norm, matrix p-norm of magic square matrix      127
Norm, monotone      119
Norm, subordinate matrix      120 121
Norm, unitarily invariant      121
Norm, vector      118—119
Norm, vector, norm equivalence constants      121t
Normal equations, error analysis      397—399
Notation, explanation of      2—3 73—76
Notay, Yvan      329
NPSOL      197
Numerical analysis, definition      6
Numerical radius      350
Numerical stability for linear equation solvers      141—142
Numerical stability, definition      8 33
Oberaigner, W.      98
Oettli — Prager backward error theorem      135
Oettli, W.      135 145
Ofman, Yu.      461
Olesky, D. D.      198
Oliver, J.      113 440
Olkin, Ingram      527
Olshevsky, V.      440 441
Olver, F. W. J.      53 76 84 113 190
Omladic, Matjaz      225
Opfer, Gerhard      441
Optimization, references for rounding error analysis      32
Ordinary differential equations, accuracy of mesh point formation      101
Ordinary differential equations, backward error in      33
Ordinary differential equations, Euler’s method with compensated, summation      95
Ordinary differential equations, references for rounding error analysis      32
Ortega, James M.      384
Osborne, M. R.      421
Ostrowski, A. M.      350 546
Outer product, error analysis      71
Overflow      18 42
Overflow, avoiding      502—504
O’Cinneide, Colm Art      147
O’Leary, Dianne Prost      305
P-norm power method      291—294 304
Paige, C. C.      225 379 385 388 397 411 415q 421 422 570
Palmer, John      525
Palmer, Kenneth J.      32
Pan, Victor      441 448 450 459
Papadimitriou, Pythagoras      386
Papadopoulos, Philip M.      323
Parallel prefix operation      165
Paranoia code      497—498
Park, Haesun      385
Parlett, Beresford N.      xxiv xxviii 27 34 58 87q 187 219 225 361q 383—385
Partial differential equations, references for rounding error analysis      32
Partial pivoting      170 173
Partial pivoting, early use of      196
Partial pivoting, growth factor      177—183
Partial pivoting, growth factor, large growth in practical problems      178
Partial pivoting, threshold pivoting      200
Partitioned algorithm, definition      246
Partitioned LU factorization, error analysis      248—250
Pascal matrix      520—524
Pascal matrix, Cholesky factor      521
Pascal matrix, inverse      522
Pascal matrix, total positivity      523
Pasternak, Mary E.      488
Patashnik, Oren      87q 520
Patrick, Merrell L.      226
Patriot missile software problem      506—507
Patterson, David A.      39n 57
Paxson, Vern      61
Pelz, Richard      505
Pena, J. M.      192 196
Pentium chip, division bug      59
Pereyra, Victor      434 436 441
Performance profile, for LAPACK norm estimator      296—297
Perturbation theory by calculus      144—145
Perturbation theory, linear systems      131—150
Perturbation theory, statistical      147 149—150
Perturbation theory, Sylvester equation      318—320
Peters, G.      113 196 279 284 287 411
Peterson, Brian      197
Philippe, Bernard      385
pi $(\pi)$, high precision calculation as computer test      49lq
Pichat, M.      98
Pierce, Daniel J.      301
Piessens, Robert      32
Pinkus, Allan      32 190 196
Plemmons, Robert J.      147 198 301 337 411 422 471 579q 580
Polar decomposition      386 389
Poljak, Svatopluk      140
Polman, Ben      257
Polynomials      103—115 (see also “Horner’s method”)
Polynomials, divided differences      109—112
Polynomials, fast evaluation schemes      114 115
Polynomials, Newton form      109—112
Ponceleon, Dulce B.      226
Poromaa, Peter      305 320 324
PORT library, machine constants      500
Portability of software      499—502
Positive definite matrix      see “Nonsymmetric positive definite matrix; symmetric positive definite matrix”
Pothen, Alex      165
Powell, M. J. D.      225 411 474 477
Power method      26
Power method for matrix 1-norm estimation      294—297
Power method for matrix p-norm estimation      291—294 304
Power, Stephen      224
Powers of a matrix      345—359
Powers of a matrix in exact arithmetic      346—353
Powers of a matrix in finite precision arithmetic      353—358
Powers of a matrix, behaviour of stationary iteration      358
Powers of a matrix, departure from normality      351—352
Powers of a matrix, hump      348—349
Powers of a matrix, pseudospectrum      352 356—358
Powers of a matrix, role of spectral radius      346—348
Prager, W.      135 145
Precision, effect of increasing      19—21
Precision, versus accuracy      7 33
Press, William H.      479 490 507
Priest, Douglas M.      33 34 58 96—99 102 502 504 531
Program verification, applied to error analysis      488
Pryce, J. D.      76 242
Pseudo-inverse      392 409 412 416
Pseudospectrum      352 356—358
Pseudospectrum of companion matrix      526
Puglisi, Chiara      371
Pukelsheim, Friedrich      323
Puschmann, Heinrich      197
Pythagorean sum      503 511—512
QR factorization      361—389
QR factorization, column pivoting      387
QR factorization, Givens      371—373
QR factorization, Givens, cancellation of errors in      24—26
QR factorization, Givens, error analysis      373—375
QR factorization, Householder      363—364
QR factorization, Householder, error analysis      368—369
QR factorization, Householder, error analysis for application to LS problem      395—396
QR factorization, Householder, error analysis for partitioned (WY representation)      370—371
QR factorization, iterative refinement for linear system      375—376
QR factorization, perturbation theory      381—383
QR factorization, rank-revealing      386
Quadratic equation, solving      11—12 33
Quadrature, accuracy of grid formation      101
Quadrature, error bound for evaluation of rule      86
Quadrature, references for rounding error analysis      32
Quarteroni, Alfio      32
Quinlan, Gerald D.      96
Quinn, Thomas R.      96
Rabinowitz, Philip      32 100
Rail, Louis B.      409 486 488
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