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Ortega J. M. — Iterative Solution of Nonlinear Equations in Several Variables
Ortega J. M. — Iterative Solution of Nonlinear Equations in Several Variables

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Название: Iterative Solution of Nonlinear Equations in Several Variables

Автор: Ortega J. M.

Аннотация:

Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time.

Although the field has developed since the book originally appeared, it remains a major background reference for the literature before 1970. In particular, Part II contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Over the years semilocal convergence results have been obtained for various methods, especially with an emphasis on error bounds for the iterates. The results and proof techniques introduced here still represent a solid basis for this topic.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 572

Добавлена в каталог: 26.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A-orthogonal vectors      260 266
Aalto, S.      523
Ablow, C.      523
Absolute value of matrices      52
Absolute value of vectors      52
Adachi, R.      523
Affine mapping      34
Agaev, G.      523
Ahamed, S.      523
Akhieser, N.      26 523
Akilov, G.      65 74 82 188 390 406 414 428 522 538
Albrecht, ].      446 447 523
Alexandroff, P.      154 155 523
Allen, B.      26 523
Almost linear mapping      11
Alternating direction (ADI) method      (see Peaceman-Rachford method)
Altman principle      251 258 259 483 496— 498
Altman, M.      164 188 258 429 493 499 500 523 524
Ambartsumanian, V.      18
Ames, W.      524
Anderson, D.      200 204 524
Anselone, P.      20 37 429 521 524
Antitone mapping      52
Antosiewicz, H.      525
Apostol, T.      65 73 81 82 169 170 521 525
Approximate contraction      393—400
Apslund, E.      88 525
Armijo, L.      493 499 525
Asymptotically monotone on rays      169
Avila, J.      341 525
Axelson, O.      525
Baer, R.      265 525
Bailey, P.      12 525
Balakrishnan, A.      525
Balazs, M.      537
Ball      2
Baluev, A.      446 454 525
Banach space      50 74 82 88 89 124 125 131 139 145 160 163 164 167 187 188 201 235 286 306 307 341 363 364 390 407 414 428 493 499
Banach, S.      125 390 525
Bard, Y      249 525
Barnes, ].      200 212 525
Bartis, M.      525
Bartle, R.      406 525
Basic types of matrices      34—36
Beale, E.      525
Beightler, C.      556
Bellman, R.      37 139 188 201 222 429 525 526
Belluce, L.      125 526
Bel’tjukov, B.      526
Ben — Israel, A.      270 406 526
Bennett, A.      428 526
Berezin, I.      390 393 446 526
Berge, C..      88 89 526
Berman algorithm      276—278
Berman, G.      276 526
Bernstein polynomial      172
Bers, L.      16 165 222 440 526
Bezlyudnaya, L.      526
Bilinear mapping      75
Birkhoff, G.      32 439 471 526 527
Birkhoff, G. D.      526
Bittner, E.      526
Bittner, L.      200 235 378 429 527
Bliss, G      26 527
Block, H.      527
Block-tridiagonal matrix      16
Blum, E.      499 527
Blundell, P.      527
Blutel, E      316 527
Bohl, E.      439 446 527
Bondarenko, P.      527
Booth, A.      258 527
Booth, R.      527
Bosarge, W      235 341 527
Boundary value theorem      157
Boundary-value problem      112 141 386 471
Boundary-value problem, elliptic      14—18 112 222 225 344 440 459 463
Boundary-value problem, two-point      9—14 23 111 116 145 201 235 344 392 393 454
Box, M      266 527 528
Braess, D      499 507 528
Bramble, J.      17 58 164 528
Brandler, F.      528
Brannin, F.      528
Brauer, F.      528
Brouwer fixed point theorem      161 164
Brouwer, L      154 155 163 528
Browder, F.      125 168 407 528
Brown, K.      228 229 528
Broyden, C.      212 213 529
Brumberg, V.      529
Bryan, C.      222 431 529
Bryant, V.      529
Budak, B.      529
Bueckner, H.      529
Buehler, R      264 552
Bussmann, K.      428 529
Cacciopoli, R.      139 390 529
Caspar, J.      145 391 529
Cauchy — Schwarz inequality      39
Cauchy, A.      97 247 258 316 390 499 529
Cavanagh, R.      317 353 429 430 529
Cesari, L.      529
Chain rule      62
Chandrasekhar, S.      18 21 529
Change of variable theorem      169
Chaplygin method      446
Characteristic polynomial      35 37
Chebyshev approximation      25
Chen, K      203 363 429 529
Chen, W      529
Cheney, E      25 406 529
Chernoff, H      188 247 248 258 499 507 530
Chu, S.      391 529 530
Ciarlet, P.      26 530
Coercive mapping      165—169
Coerciveness theorem      166
Coffman, C.      306 530
Collatz, L      188 201 390 399 420 429 439 446 471 521 530
Compact support      149 155
Comparable vectors      51
Comparison principle for steplength algorithms      484
Composite mapping      62
Concus, P.      31 530
Condition number      42
Conjugate basis      260
Conjugate vectors      260
Conjugate-direction methods      260—267 509—513
Conjugate-gradient method      261—263 271 273 509—513
Connected functional      98—101 105 108
Consistent approximation      355—369 371 375
Consistently ordered matrix      344
Conte, S.      228 528
Continuation method      230—236 334—341
Continuation property      132—141
Continuous differentiability      60 71
Continuous iterative process      235
Contraction      119—125 164 408 433 439
Contraction mapping theorem      120 124 125 385 410
Contraction mapping theorem, generalizations      164 383—408
Contraction, approximate      393—400
Contraction, iterated      400—401 406—407
Contractions, sequence of      393 400
Control problem      12
Convergence factor      281—298 (see also Q-factor R-factor)
Convergence of iterative methods      (see Particular method)
Convergence theorem, types of      5 (see also Various theorems (global local monotone semilocal
Convex functional      82—90 99—109 142
Convex mapping      448—450 454 455
Coordinate vector      34
Critical point      93—98 100 101 473—520
Crockett, J.      188 247 248 258 499 507 530
Cronin, J.      155 160 530
Cryer, C.      530
Cube in R      130
Curry principle      251 258 483 496—498
Curry, H      258 493 499 530
Damped methods      (see Particular method)
Damping factor      253
Daniel algorithm      262 509
Daniel algorithm, convergence      509 510
Daniel, J.      265 512 530
Daugavet, I.      530
Davidenko, D.      235 530 531
Davidon, W.      212 248 531
Davis, J.      235 531
de Figueiredo, D.      168 531
Degree integral      149 151
Degree of mapping      147—160 82
Degree of mapping, process      200
Deist, F.      235 531
Dennis, J.      406 528 531
Derendjaev, I.      531
Derivative      (see also F-derivative G-derivative)
Derivative, higher order      75 81
Descent method      243 473
Diagonal dominance theorem      48
Diagonal mapping      11
Diagonally dominant matrix      48
Diagonally isotone mapping      464
Diaz, J.      390 391 407 527 529 530 531
Dieudonn      6
Difference equation      238 294 305 306 353 409 420
Differential      (see Frechet differential Gateaux
Differential correction method      (see Gauss — Newton method)
Differential inequalities for convexity      84 88 448—450
Differentiation with respect to a parameter      235
Direction vector      244
Dirichlet problem      14
Discrete analog      10 15 19
Discrete Newton method      (see Newton method)
Discrete Ritz method      24 26 27
Discretization error      12 16
Divergence theorem      170
Divided difference operator      201—203 213 363
Dolph, C.      164 531
Domain of iterative process      236
Domain-invariance theorem      145 160
Douglas, J., Jr.      222 391 531
Draper, N.      25 531
Dressel, H.      551
Dreyfus, S.      531
Dubovik, L.      531
Duck, W      532
Duleau, J.      532
Dulley, D.      532
Dunford, N.      163 532
Durand, E.      307 532
D’jakonov, Ye.      531
Edelstein, M.      406 532
Edmunds, D.      532
Eggleston, H.      88 532
Ehrmann, H.      139 399 532
Eigenvalue      35
Eigenvector      35
Elkin, R      89 101 102 103 108 265 275 478 493 494 499 500 507 508 518 519 520 532
Elliptic boundary value problem      14—18 112 222 225 344 440 454 463
Elliptic norm      245
Ellipticity condition      17 30 31
Emelina, L.      532
Essentially periodic sequence      513—516
Euclidean norm      39
Euler equation      22 26 30 31
Euler’s method      233—235 339
Excision theorem      158
F-derivative      61 62 65—67
F-derivative, partial      127 128 131 132
F-derivative, second      75—81
F-derivative, strong      71 72 74 126 127 131
f-function      (see Forcing function)
F-minimal solution      96
Faddeev, D.      37 44 532
Faddeeva, V.      37 44 532
Falb, P.      527
Farforovskaya, J.      534
Feder, D      532
Feldstein, A.      286 532
Fel’dman, I.      532
Fenchel, W.      88 101 532
Fenyo, I.      533
Fiacco, A.      533
Fibonaccian search      276—278
Ficken, F      139 234 533
Filippi, S.      533
Fine, H      428
Firestone, R.      286 532
First integral of difference equation      416
Fixed point      119
Fleming, W.      533
Fletcher — Reeves algorithm      262 510
Fletcher — Reeves algorithm, convergence      510 511
Fletcher, R.      212 213 248 265 273 533
Flood, M.      533
Fok, V.      235
Fomin, S.      390 540
Forcing function      479
Forster, P.      533
Forsythe, G      16 222 307 343 521 533
Fox, L.      533
Frank, T.      18 533
Frechet derivative      (see F-derivative)
Frechet differential      66
Frechet, M.      533
Free steering sequence or method      223 513 517 519
Freudenstein, F.      235 533
Frey, T      533
Fridman, V      270 533
Fridrih, F.      533
Fujii, M.      5
Function      (see Mapping)
Functional averaging method      226
Functional, connected      98—101 105 108
Functional, convex      82—90 99—109 142
Functional, hemivariate      474 475 478 479
Functional, midpoint convex      89
Functional, pseudoconvex      102—104 518
Functional, quasiconvex      99—105 108 275 479 489
Fundamental theorem of integral calculus      70
G-derivative      59—62 65—67 71 74
G-derivative, second      75—81 87
Gagliardo, E.      534
Galanov, B.      534
Gale, D.      140 145 534
Gantmacher, F.      37 534
Gardner, G      399 534
Gateaux derivative      (see G-derivative)
Gateaux differential      65 66
Gateaux, R.      534
Gauss method      (see Gauss-Newton method)
Gauss — Newton method      227 267—270
Gauss — Newton method, convergence      320 505 506
Gauss — Newton method, damped      503
Gauss — Seidel principle      224
Gauss, K.      200
Gauss-secant method      269
Gauss-Seide! method      (see SOR method)
Gauss-Seidel-Newton method      (see SOR-Newton method)
Gaussian elimination      227
Gavurin, M.      235 534
Gendzojan, G.      534
General position      191
1 2 3 4
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