numerical analysis algorithms

/P 495 0 R /K [ 87 ] >> /P 996 0 R 745 0 obj /K [ 753 0 R ] /Type /StructElem >> 725 0 obj /Dialogsheet /Part /K [ 283 ] /Type /StructElem /Type /StructElem 1177 0 obj /P 929 0 R /Type /StructElem /S /LBody /S /P /P 299 0 R endobj /Pg 34 0 R /P 1350 0 R << /Pg 49 0 R << /S /TD /K [ 995 0 R ] /Type /StructElem endobj << /P 258 0 R << /K [ 609 0 R 611 0 R 613 0 R 615 0 R 617 0 R 619 0 R 621 0 R 623 0 R ] /Type /StructElem /P 739 0 R /K [ 118 ] >> << /K [ 6 ] >> /Pg 63 0 R >> endobj /S /P /K [ 1013 0 R ] /Pg 49 0 R << /S /TR /Type /StructElem /Pg 57 0 R >> /P 771 0 R /Pg 44 0 R << /Type /StructElem << /P 1114 0 R /P 72 0 R A rough categorization of the principal areas of numerical analysis is given below, keeping in mind that there is often a great deal of overlap between the listed areas. >> << /Pg 44 0 R 288 0 obj /Pg 57 0 R 487 0 obj /K [ 251 ] /S /TD /K [ 84 ] 1349 0 obj /Type /StructElem endobj /Pg 57 0 R /Pg 57 0 R /Type /StructElem /P 575 0 R >> /Type /StructElem >> /P 193 0 R endobj /Pg 54 0 R /Type /StructElem /S /P /P 1256 0 R /K [ 252 0 R ] >> /Pg 63 0 R /K [ 1443 0 R ] >> endobj /P 822 0 R << (2017) Iterative Methods Based on Soft Thresholding of Hierarchical Tensors. /Pg 63 0 R /S /TD CCD implementation. << /K [ 46 ] /Pg 49 0 R /K [ 6 ] (2020) Numerical subspace algorithms for solving the tensor equations involving Einstein product. << /Pg 57 0 R /S /TD >> /K [ 999 0 R ] /Type /StructElem 1051 0 R 1053 0 R 1055 0 R 1056 0 R 1059 0 R 1061 0 R 1063 0 R 1065 0 R 1067 0 R /K [ 59 ] /Type /StructElem 1069 0 obj << endobj Often we do not fully understand the characteristics of a problem, especially very complicated and large ones. /S /P /K [ 89 ] /Pg 46 0 R /P 1263 0 R 4 0 obj /Type /StructElem /Pg 63 0 R /S /P /P 72 0 R /P 72 0 R /K [ 673 0 R ] /P 72 0 R /Pg 54 0 R /Pg 44 0 R 1940's, the growth in power and availability of digital computers 162 0 obj /Type /StructElem /P 72 0 R >> /P 1416 0 R endobj >> 846 0 obj 327 0 obj /Pg 54 0 R /K [ 17 ] /Pg 63 0 R >> >> /P 548 0 R /P 488 0 R /HideWindowUI false endobj /Type /StructElem Instead, the Regula-Falsi method should test the condition |x-a|> /Type /StructElem /K [ 671 0 R ] /Pg 44 0 R >> /Pg 44 0 R /S /P /K [ 1415 0 R ] /P 880 0 R >> /P 998 0 R 628 0 obj /Pg 34 0 R >> /P 842 0 R << endobj endobj << /Pg 63 0 R /K [ 1271 0 R ] endobj 348 0 R 350 0 R 352 0 R 353 0 R 356 0 R 358 0 R 360 0 R 362 0 R 364 0 R 366 0 R 368 0 R /P 72 0 R << /K [ 324 0 R ] /P 1479 0 R >> /Type /StructElem /P 72 0 R 460 0 obj in which \(f^{\prime}(x)\) denotes the Jacobian matrix, of order \(m\times m\) for \(f(x)\ .\), In practice, the Jacobian matrix for \(f(x)\) is often too complicated to compute directly; instead the partial derivatives in the Jacobian matrix are approximated using 'finite differences'. 1442 0 obj /Pg 54 0 R /K [ 9 ] endobj /P 723 0 R >> << endobj 595 0 obj /P 322 0 R /P 251 0 R /S /TD /S /P /P 463 0 R >> /Type /StructElem /K [ 120 0 R 122 0 R ] >> /P 381 0 R /K [ 237 ] /K [ 1217 0 R ] 1253 0 obj >> /P 448 0 R /Pg 54 0 R 652 0 obj /Pg 49 0 R endobj << /S /TD >> /F1 5 0 R /K [ 282 0 R ] /Pg 46 0 R /K [ 75 ] 757 0 obj /Type /StructElem /S /P /S /P >> /S /TD << 601 0 obj /K [ 72 ] /K [ 26 ] /Pg 57 0 R endobj 121 0 obj /Pg 54 0 R /S /P /Type /StructElem /S /TD Cubature of Multidimensional Schrödinger Potential Based on Approximate Approximations. /S /P endobj 1057 0 obj << 1286 0 R 1287 0 R ] /S /P 411 0 obj /S /TD endobj endobj /K [ 209 ] endobj /P 430 0 R /K [ 25 ] /Type /StructElem /K [ 63 ] /P 597 0 R 677 0 obj /Type /StructElem 1321 0 obj /S /P /Pg 57 0 R /Pg 57 0 R >> 1146 0 obj /Pg 57 0 R /Type /StructElem Dr. Kendall E. Atkinson, Department of Computer Science, Department of Mathematics, University of Iowa. /Pg 49 0 R endobj /P 1368 0 R /Pg 34 0 R >> /Pg 44 0 R /Type /StructElem /K [ 46 ] 605 0 obj >> << Encyclopedia of Applied and Computational Mathematics, 1060-1066. /Pg 63 0 R /Type /StructElem /S /TR 1493 0 obj 625 0 R 626 0 R 635 0 R 636 0 R 637 0 R 638 0 R 639 0 R 640 0 R 641 0 R 642 0 R 643 0 R >> /Type /StructElem 382 0 obj 185 0 obj endobj /Pg 63 0 R << 1091 0 obj /P 221 0 R >> >> /Pg 63 0 R >> 1334 0 obj endobj /Type /StructElem /Pg 57 0 R /K [ 70 ] /S /TD /Type /StructElem 440 0 obj /Type /StructElem << /K [ 931 0 R ] /K [ 659 0 R 675 0 R 691 0 R 707 0 R 723 0 R 739 0 R 755 0 R 771 0 R 787 0 R 803 0 R endobj << /K [ 102 ] Non-Concurrent Computational Homogenization of Nonlinear, Stochastic and Viscoelastic Materials. endobj 736 0 obj >> /S /P << /Type /StructElem /Pg 3 0 R endobj endobj /P 587 0 R endobj /K [ 1496 0 R ] >> /Pg 34 0 R /S /Span /K [ 276 ] /Type /StructElem /P 386 0 R << /Pg 57 0 R /K [ 86 ] /P 1351 0 R /Type /StructElem >> 655 0 obj /Pg 49 0 R << 1360 0 obj << 120 0 obj /P 675 0 R << /Pg 44 0 R /Pg 54 0 R /K 82 /K 303 endobj /Type /StructElem /S /TD /K [ 42 43 44 45 46 47 48 49 50 ] /P 72 0 R /Type /StructElem /S /P 448 0 obj endobj /S /P /K [ 59 ] /K [ 29 ] /P 750 0 R /Type /StructElem /P 1199 0 R /Pg 46 0 R /Type /StructElem /S /P /P 1135 0 R /Type /StructElem /Type /StructElem endobj endobj >> << 989 0 obj /Type /StructElem >> endobj >> >> /P 1335 0 R /Type /StructElem /Type /StructElem << >> endobj /P 242 0 R endobj endobj endobj << endobj << /Pg 57 0 R /S /TD /P 1480 0 R /K [ 259 ] 973 0 obj 413 0 obj /K [ 270 0 R ] /Pg 57 0 R >> 1167 0 obj 938 0 obj /Type /StructElem endobj endobj >> endobj /Type /StructElem /K [ 97 ] endobj /P 787 0 R /Type /StructElem /S /P /Pg 3 0 R >> << endobj endobj /F3 12 0 R << /K [ 1283 0 R 1284 0 R 1285 0 R 1286 0 R 1287 0 R ] /Pg 57 0 R >> /S /P >> << >> sophistication has been needed to solve these more accurate and complex << /S /Span Machine Learning and Knowledge Discovery in Databases, 458-473. /Pg 49 0 R /K 280 >> /Pg 46 0 R /S /P >> /Type /StructElem endobj /P 490 0 R /Pg 54 0 R /Pg 57 0 R /P 1167 0 R /Type /StructElem /S /P /Type /StructElem << >> /K [ 1356 0 R ] /P 986 0 R /Pg 44 0 R endobj /P 306 0 R << /Pg 54 0 R /P 611 0 R << (2012) Multiresolution representation of operators with boundary conditions on simple domains. /Pg 44 0 R /P 72 0 R endobj endobj (2016) Numerical methods for high-dimensional probability density function equations. 274 0 obj /P 527 0 R /Type /StructElem endobj /S /TD /K [ 221 ] /Pg 54 0 R /P 1184 0 R /S /TD /Pg 57 0 R 539 0 R 541 0 R 542 0 R 545 0 R 547 0 R 549 0 R 551 0 R 553 0 R 555 0 R 557 0 R 558 0 R /Type /StructElem /P 658 0 R /Type /StructElem << /Type /StructElem /P 1395 0 R /Pg 54 0 R /S /P endobj 389 0 obj << >> /K 256 >> /Pg 49 0 R 1431 0 obj /K [ 811 0 R ] /S /P /K [ 881 0 R 897 0 R 913 0 R 929 0 R 945 0 R 961 0 R 977 0 R 993 0 R 1009 0 R 1025 0 R 1240 0 obj /Type /StructElem /P 1052 0 R /Type /StructElem >> 462 0 obj /Type /StructElem /Pg 57 0 R >> /S /P /Pg 3 0 R /K [ 222 0 R ] /Pg 46 0 R /Type /StructElem >> /K [ 38 ] endobj endobj