/P 724 0 R << << << /S /P /K [ 1419 0 R ] /Pg 54 0 R /Pg 34 0 R /K [ 32 ] /Type /StructElem 1224 0 obj << >> << endobj /Pg 60 0 R 672 0 obj /S /LI << /Type /StructElem /Pg 63 0 R >> /S /TD >> << /S /P /F1 5 0 R << /Type /StructElem /S /Figure << >> /Alt () 1026 0 obj endobj 774 0 obj /P 566 0 R 422 0 R 423 0 R 424 0 R 425 0 R 426 0 R 427 0 R 428 0 R 429 0 R 430 0 R 624 0 R 625 0 R << >> >> endobj /Pg 54 0 R >> /S /P 323 0 obj The various ways of doing this lead to 'Galerkin methods', 'collocation methods', and 'least square methods'. /Pg 57 0 R 1314 0 obj endobj /Type /StructElem >> /Type /StructElem /Type /StructElem /Pg 49 0 R /Pg 57 0 R << >> << 1411 0 obj /P 1418 0 R /S /P /P 977 0 R endobj << /K [ 683 0 R ] /Pg 34 0 R >> /K [ 254 ] /P 1041 0 R >> /Pg 49 0 R /P 527 0 R /K [ 70 ] /Pg 57 0 R << /K [ 117 ] /S /P /K [ 569 0 R ] /S /TD << >> << /Pg 57 0 R /K [ 318 0 R ] << /K [ 724 0 R 726 0 R 728 0 R 730 0 R 732 0 R 734 0 R 736 0 R 738 0 R ] /K [ 74 ] endobj >> /S /TD << >> \[ /K [ 263 ] 921 0 obj /Type /StructElem endobj 1011 0 obj /S /P << 352 0 obj >> endobj /Type /StructElem /P 1087 0 R << /S /LBody 1480 0 obj << /Pg 44 0 R >> /S /P endobj >> /Pg 49 0 R 1377 0 obj /Type /StructElem /S /Span >> /Pg 57 0 R << /S /TD endobj /K [ 86 ] /Type /StructElem /K [ 110 ] << endobj >> /P 766 0 R /K [ 708 0 R 710 0 R 712 0 R 714 0 R 716 0 R 718 0 R 720 0 R 722 0 R ] /P 803 0 R /K [ 733 0 R ] /Pg 57 0 R /Type /StructElem >> >> /S /H2 113 0 obj /P 237 0 R /Type /StructElem She has contributed software to LAPACK, ScaLAPACK, and the MATLAB distribution. /Type /StructElem /P 897 0 R /Pg 44 0 R /S /P 311 0 obj /Pg 54 0 R << /QuickPDFF4a2081a7 29 0 R /P 552 0 R /K [ 889 0 R ] /Type /StructElem /Pg 49 0 R endobj << >> /S /P /P 511 0 R 364 0 obj 169 0 obj << endobj 871 0 obj >> endobj /Type /StructElem >> << /Type /StructElem 503 0 obj /P 431 0 R /Pg 44 0 R /P 1041 0 R >> /P 370 0 R /S /TD /K [ 109 ] endobj endobj << /Type /StructElem 1340 0 obj << /P 322 0 R /Pg 49 0 R << << 1201 0 obj 1428 0 obj /Pg 46 0 R /S /TD endobj << /S /LBody endobj /P 1368 0 R /K 240 /Type /StructElem /Pg 54 0 R >> endobj endobj << /Pg 57 0 R endobj >> /Pg 57 0 R /P 72 0 R /P 1174 0 R /K [ 52 ] /P 72 0 R endobj /K [ 3 ] >> Errors in Numerical Computations Introduction Preliminary Mathematical Theorems Approximate Numbers and Significant Figures Rounding Off Numbers Truncation Errors Floating Point Representation of Numbers Propagation of Errors General Formula for Errors Loss of Significance Errors Numerical Stability, Condition Number, and Convergence Brief Idea of Convergence, Numerical Solutions of Algebraic and Transcendental EquationsIntroduction Basic Concepts and Definitions Initial ApproximationIterative Methods Generalized Newton’s Method Graeffe’s Root Squaring Method for Algebraic Equations, Interpolation Introduction Polynomial Interpolation, Numerical Differentiation Introduction Errors in Computation of Derivatives Numerical Differentiation for Equispaced Nodes Numerical Differentiation for Unequally Spaced Nodes Richardson Extrapolation, Numerical Integration Introduction Numerical Integration from Lagrange’s Interpolation Newton–Cotes Formula for Numerical Integration (Closed Type) Newton–Cotes Quadrature Formula (Open Type) Numerical Integration Formula from Newton’s Forward Interpolation Formula Richardson Extrapolation Romberg Integration Gauss Quadrature Formula Gaussian Quadrature: Determination of Nodes and Weights through Orthogonal Polynomials Lobatto Quadrature Method Double Integration Bernoulli Polynomials and Bernoulli NumbersEuler–Maclaurin Formula, Numerical Solution of System of Linear Algebraic Equations Introduction Vector and Matrix Norm Direct MethodsIterative Method Convergent Iteration Matrices Convergence of Iterative Methods Inversion of a Matrix by the Gaussian Method Ill-Conditioned Systems Thomas Algorithm, Numerical Solutions of Ordinary Differential Equations Introduction Single-Step Methods Multistep Methods System of Ordinary Differential Equations of First Order Differential Equations of Higher Order Boundary Value Problems Stability of an Initial Value Problem Stiff Differential Equations A-Stability and L-Stability, Matrix Eigenvalue Problem Introduction Inclusion of Eigenvalues Householder’s Method The QR Method Power Method Inverse Power Method Jacobi’s Method Givens Method, Approximation of Functions Introduction Least Square Curve Fitting Least Squares Approximation Orthogonal Polynomials The Minimax Polynomial Approximation B-Splines Padé Approximation, Numerical Solutions of Partial Differential Equations Introduction Classification of PDEs of Second Order Types of Boundary Conditions and Problems Finite-Difference Approximations to Partial Derivatives Parabolic PDEs Hyperbolic PDEs Elliptic PDEs Alternating Direction Implicit Method Stability Analysis of the Numerical Schemes, An Introduction to the Finite Element Method Introduction Piecewise Linear Basis Functions The Rayleigh–Ritz Method The Galerkin Method. 1213 0 obj >> 85 0 obj >> << >> /K [ 68 ] /S /P >> 427 0 obj /S /P /Type /StructElem 958 0 obj endobj /Type /StructElem /Pg 44 0 R endobj << 1382 0 obj /P 527 0 R /Type /StructElem 920 0 obj /K [ 34 ] endobj /S /P /K [ 775 0 R ] /S /TD /S /Span /Pg 54 0 R endobj << 1468 0 obj /Type /StructElem endobj << 161 0 obj (2020) Krylov subspace projection method for Sylvester tensor equation with low rank right-hand side. 1308 0 obj << /K [ 600 0 R ] /P 1263 0 R << << endobj /S /TR << /Pg 46 0 R /S /P >> /K [ 100 ] endobj /K [ 28 ] \tilde{u}_{n}(0)=\tilde{u}_{n}(1)=0 /S /TD 1315 0 obj /Type /StructElem /P 908 0 R /P 601 0 R /S /Span /S /TR /Pg 54 0 R endobj 1396 0 obj endobj /Type /StructElem 496 0 obj endobj 1177 0 R 1179 0 R 1181 0 R 1182 0 R 1185 0 R 1187 0 R 1189 0 R 1191 0 R 1193 0 R /K [ 805 0 R ] 1328 0 obj /Type /StructElem /S /LI endobj /Pg 49 0 R << 933 0 obj /Type /StructElem /Pg 49 0 R /K [ 91 ] endobj endobj << /P 880 0 R endobj /Type /StructElem /K [ 105 ] >> /S /TD /Type /StructElem /K [ 1433 0 R ] /S /Figure << /S /P /P 221 0 R << endobj /P 486 0 R endobj /Pg 57 0 R 131 0 obj /P 72 0 R /K [ 252 0 R ] >> << /Pg 44 0 R endobj /S /LI << << << /Pg 46 0 R /P 274 0 R << (2012) Multiresolution representation of operators with boundary conditions on simple domains. /Pg 44 0 R 148 0 R 149 0 R 150 0 R 151 0 R 152 0 R 153 0 R 154 0 R 155 0 R 156 0 R 157 0 R 158 0 R endobj 338 0 obj << /S /TD /S /P /Pg 57 0 R /S /P /K [ 93 ] /Type /StructElem /P 72 0 R /Pg 49 0 R /S /TR /K [ 553 0 R ] 1344 0 obj 1137 0 obj /Pg 44 0 R >> /Type /StructElem /K [ 260 0 R ] << 484 0 obj >> /K [ 17 ] 967 0 obj /Type /StructElem /Type /StructElem /Type /StructElem >> endobj << endobj 214 0 obj /Pg 57 0 R /K [ 8 ] endobj << >> /P 880 0 R /S /TD /Pg 57 0 R endobj /S /TD /Pg 57 0 R /Pg 34 0 R /Type /StructElem /Pg 57 0 R /P 900 0 R /Type /StructElem /Pg 63 0 R 1105 0 obj /S /P 369 0 obj 1058 0 obj endobj << (2018) Linear systems with a canonical polyadic decomposition constrained solution: Algorithms and applications. endobj endobj 434 0 obj >> << /P 72 0 R /Type /StructElem