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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
$0^0$, definition      64
$2\times 2$ problems, reliable solution of      500—501
$LDL^T$ factorization      205
$LDL^T$ factorization, block      218
$\gamma_n$ (error constant), definition      69
$\gamma_n$ (error constant), properties      74
$\infty$(IEEE arithmetic)      46—47 492 495
$\varepsilon$-pseudospectral radius      352
3M method      450 461 505
3M method, error analysis      458—459
Aasen, Jan Ole      226
Aasen’s method      226 229
Abdelmalek, Nabih N.      385 410
Abramowitz, Milton      35
Absolute error      4
Absolute norm      119
Accuracy versus precision      7 33
ACRITH      486
Acton, Forman S.      35 203q 285
Adams, Duane A.      113
Aggarwal, Vijay B.      84
Ahac, Alan A.      198
Ahlberg, J. H.      167
Aitken extrapolation      101
Aitken, A. C      383
Albers, Donald J.      513 n
Alefeld, Goltz      486
Alexopolous, Aristides G.      54
Allen, Jr., Richard C.      84
Almacany, Montana      425 q
Alternating directions method      477
Aluru, Srinivas      459
Alvarado, Fernando L.      165
Amato, James J.      323
Ames, William F.      32
Amodio, Pierluigi      197
Anda, Andrew A.      385
Anderson, E.      289 q
Anderson, T. W.      527
Ando, T.      196
Approximation theory, references for rounding error analysis      32
Arioli, Mario      143 304 328 343 410 411 421 422
Arnold, William F.      323
Ashenhurst, R. L.      489
Asplund, Edgar      305
Atanasoff, John V.      151 q
Augment precompiled      486 504 506
Augmented system matrix      393
Augmented system matrix, scaling and conditioning      402
Automatic Computing Engine (ACE)      56 189t 195 343
Automatic differentiation      488
Automatic error analysis      473—490 (see also “Interval analysis; running error analysis”)
Automatic error analysis, condition estimation      480—481
Automatic error analysis, solving a cubic      483—484
Automatic error analysis, Strassen’s inversion method      481—482
Automatic error analysis, using direct search optimization      474—477
Axelsson, Owe      343
Babuska, Ivo      100
Bachelis, Boris      61
Backward error      7—8
Backward error analysis in differential equations      33
Backward error analysis, development by Wilkinson      33—34 189
Backward error analysis, motivation      7
Backward error analysis, not a panacea      1q
Backward error analysis, purpose      71—72 203
Backward error, componentwise      134 141
Backward error, componentwise relative      134
Backward error, componentwise, evaluating      143
Backward error, definition      7
Backward error, least squares problem      404—407 413
Backward error, linear system, Oettli — Prager theorem      135
Backward error, linear system, Rigal — Gaches theorem      14 132
Backward error, Lyapunov equation      316—317
Backward error, mixed forward-backward error      8
Backward error, norm wise relative      132
Backward error, normwise      132
Backward error, preserving symmetric structure      149 406—407
Backward error, structured      141
Backward error, Sylvester equation      313—316
Backward error, underdetermined system      419 423
Backward stability, componentwise      142
Backward stability, definition      8
Backward stability, normwise      142
Bai, Zhaojun      322 352 527
Bailey, David H.      448 460 461 471 482 491q 505
Baksalary, J. K.      323 324
Ballester, C.      441
Banded matrix, growth factor      183
Bane, Susanne M.      461
Bank, Randolph E.      257
Bareiss, E. H.      53 191
Bargmann, V.      186
Barlow, Jesse L.      33 51 53 191 193 301 385 411 412
Barnett, S.      323
Barone, John L.      391q 410
Barrett, Geoff      59
Barrlund, Anders      194 198 224
Bartels — Stewart method      311—313
Bartels, R H.      312
Bartels, Sven G.      141 304 441
Barwell, Victor      226
Bauer, F. L.      57 83 119 126 139 146 148 149 191 284 551
Bauer’s scaling theorem      139 146
Beam, Richard M.      527
Beaton, Albert E.      391q 410
Bell, E. T.      281 q
Bellman, Richard      324
Benford, Frank      51
Benoit, Commandant      224
Benschop, N. F.      327
Berman, Abraham      147 579q 580
Bhatia, Rajendra      322 382
Bilinear noncommutative matrix multiplication algorithm      449—450
Bilinear noncommutative matrix multiplication algorithm, error analysis      456—457
Binary-decimal conversion      61—62
Bini, Dario      441 456 457
Birkhoff, Garrett      32 281 483
Bischof, Christian H.      299 301 370 384
Bit      60
Bj0rstad, Petter      461
Bjorck, Ake      83 242 361q 379 385 386 388 397 399 400 402 403 409—411 422 423 434 436 441 570
Blanch, G.      507
BLAS (Basic Linear Algebra Subprograms)      586—587
BLAS (Basic Linear Algebra Subprograms), fast level      3 460
BLAS (Basic Linear Algebra Subprograms), level 2 extended precision extension      506
BLAS (Basic Linear Algebra Subprograms), xnrm2 (2-norm)      502—503 510—511
Bliss, B.      488
Block algorithm, advantages of      245 q
Block algorithm, definition      246
Block diagonal dominance      251—255 257
Block diagonal dominance and block LU factorization      252—255
Block diagonal dominance, definition      251
Block LU factorization      246—259
Block LU factorization, computation      247
Block LU factorization, definition      246
Block LU factorization, error analysis      250—257
Block LU factorization, existence and uniqueness      247
Block LU factorization, stability for (point) diagonally dominant matrix      255
Block LU factorization, stability for block diagonally dominant matrix      251—255
Block LU factorization, stability for block tridiagonal matrix      258
Block LU factorization, stability for symmetric positive definite matrix      255—257
Blue, James L.      502
Bodewig, E.      188
Bohlender, Gerd      98
Bohte, Z.      183
Boley, Daniel      243
Bollen, Jo A. M.      328
Bondeli, S.      525
Boros, T.      441
Borwein, J. M.      491q
Borwein, P. B.      491q
Bowden, B. V.      203q
Bowdler, H. J.      196
Boyd, David W.      291 293 304
Boyle, Jeff      51
Brent, Richard P.      51 162 164 448 451 453 460 486 504 508
Briggs, William L.      470
Brightman, Tom      60
Brown, W. S.      498 501
Brunet, Marie-Christine      53 488
Buchan, John      62q
Buchanan, James L.      165
Buchholz, W.      60
Bukhberger, B.      305
Bulirsch, R      83 84 190
Bunch — Kaufman factorization      221—223
Bunch — Parlett factorization      219—220
Bunch, James R      141 146 149 219—221 225 226 231q
Buoni, John J.      198
Burgmeier, James W.      84
Businger, Peter A.      146 193 410
Butcher, J. C      100
Byers, Ralph      305 320 323 324 353 567
BYTE      60
Caffney, John      520
Calculator, displaying words on      37
Calve, M. P.      32
Calvetti, D.      440—442
Calvin (and Hobbes)      473q
Campbell, S. L.      337
Campbell-Kelly, Martin      245q
Cancellation      10—11 30
Cancellation in summation      91 543
Cancellation of rounding errors      21—26
Cancellation, not a bad thing      11
Canuto, Claudio      32
Cao, Wei-Lu      305
Caprani, Ole      100
Cardano, Geronimo      483
Carr III, John W.      57
Carter, Russell      496
Cauchy matrix      516—517
Cauchy matrix, inverse      516
Cauchy matrix, LDU factors      516—517
Cauchy — Schwarz inequality      119
Cauchy, Augustin-Louis      516
Cayley, Arthur      446
CELEFUNT      499
Chaitin-Chatelin, Francoise      53 358 488
Chan, Raymond H.      471
Chan, Tony F.      13 33 146 147 386
Chandrasekaran, Shivkumar      136 141 386
Chang, Xiao-Wen      225
Chaos, references for rounding error, analysis      32
Chartres, Bruce A.      190
Chatelin, Francoise      see “Chaitin-Chatelin Francoise”
Chebyshev spectral differentiation matrix      346 355
Choi, Man-Duen      513q 526
Cholesky factorization      204
Cholesky factorization, computation of      205
Cholesky factorization, conditions for success in floating point      208—209
Cholesky factorization, error analysis      205—209
Cholesky factorization, existence and uniqueness      204
Cholesky factorization, perturbation bounds      209—210
Cholesky factorization, semidefinite matrix, complete pivoting      211
Cholesky factorization, semidefinite matrix, computation of      210—211
Cholesky factorization, semidefinite matrix, error analysis      214—218
Cholesky factorization, semidefinite matrix, existence and uniqueness      210
Cholesky factorization, semidefinite matrix, perturbation theory      211—214
Cholesky factorization, semidefinite matrix, termination criteria      217—218
Cholesky, Andre-Louis      224
Chopping      57
Christiansen, S0ren      146
Chu, Eleanor      193
Chu, King-wah Eric      323
Cipra, Barry A.      32
Circulant matrix      468
Circulant preconditioned      471
Circulant system, error analysis for solution by FFT      468—470
CLAPACK      588
Clasen, B.-L      284
Clenshaw, C. W.      32 53 113
Cline, Alan K.      289q 297 299 411 480
Cline, R. E.      422
Clinger, William D.      61
Cody, Jr., William J.      39q 54 55 59 60 495 497 499 504
Cohen, A. M.      180 522
Colon notation      2—3
Companion matrix      525—526
Companion matrix, singular values      525—526
Comparison matrix      157
Compensated summation      92—97
Complete pivoting      170
Complete pivoting, early use of      196
Complete pivoting, fallacious criticism of      200
Complete pivoting, growth factor      180—181 197
Complete pivoting, growth factor, conjecture proved false      181
Complex arithmetic, error analysis      78—80 84
Complex number, division without overflow      503—504 509
Complex number, square root of      36
Componentwise relative error      5
Concus, P.      257
Condition number of function      9
Condition number of linear system, componentwise      135
Condition number of linear system, normwise      133
Condition number of rectangular matrix      392
Condition number of square matrix      121—123 126
Condition number of summation      100
Condition number, distance to singularity and      123 126 140
Condition number, estimation      289—308
Condition number, estimation for tridiagonal matrices      301—303
Condition number, estimation, counterexamples      289q 294—296 299 304 305
Condition number, estimation, counterexamples by direct search      480—481
Condition number, estimation, incremental      301
Condition number, estimation, LAPACK estimator      294—297 480—481
Condition number, estimation, probabilistic methods      300—301
Condition number, estimation, UNPACK estimator      297—299
Condition number, general theory      33
Condition number, Hadamard      281 287
Condition number, minimizing by scaling      136—139 146
Condition number, Skeel’s      135
Conjugate gradient method      328 329 341
Conte, Samuel D.      190
Continued fraction, algorithms and error analysis      507
Continued fraction, evaluating in IEEE arithmetic      492—493
Continued fraction, running error bound      85
Convergent matrix      348
Conversion, binary-decimal      61—62
Cooley, James W.      470
Coomes, Brian A.      32
Coonen, Jerome T.      59 495
Cope, J. E.      145
Coppersmith, Don      448
Corless, Robert M.      32
Corm, Andrew R.      299
Correct significant digits      4—5 32
Cortes, Joaquin      197
Cottle, Richard W.      224
Cox, M. G.      32
Cramer’s rule, (instability of      14—15 34 37
Cray computers, adoption of IEEE arithmetic      49
Cray computers, arithmetic on      39q 495
Cray computers, puzzling results from Cray Y-MP and Cray 2      496—497
Cray computers, UNICOS library      448 450
Crout, Prescott D.      195
Crout’s method      174
Cryer, Colin W.      180 181 196
CS decomposition      388 408
Cubic equation, Newton’s method      489—490
Cubic equation, stability of explicit formulae for roots      483—484
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