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Trefethen L.N., Bau D. — Numerical Linear Algebra
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Название: Numerical Linear AlgebraАвторы: Trefethen L.N., Bau D. Аннотация: Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra. Designed for use as a stand-alone textbook in a one-semester, graduate-level course in the topic, it has already been class-tested by MIT and Cornell graduate students from all fields of mathematics, engineering, and the physical sciences. The authors' clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2002Количество страниц: 361Добавлена в каталог: 07.04.2008Операции: Положить на полку |
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Matrix, positive definite see "Hermitian positive definite matrix" Matrix, random 96 114 167—171 189 233 240 244 262 271 334 Matrix, random orthogonal 65 114 120 Matrix, random sparse 300 309 Matrix, random triangular 96 128 167 Matrix, skew-Hermitian 16 187 Matrix, sparse 232 244 300—301 Matrix, symmetric 11 172 Matrix, Toeplitz 68 318 337 342 Matrix, triangular 10 15 49 240 Matrix, tridiagonal 194 218 Matrix, unit triangular 62 148 Matrix, unitarily diagonalizable see "Normal matrix" Matrix, unitary 14—16 119 163 187 Matrix, Vandermonde 4 53 64 78 137 289 292 337 Matrix, well-conditioned 94 matrix-matrix multiplication 5 matrix-vector multiplication 3 93 330 Memory hierarchy 59 Minres 293 Multigrid methods 317 326 Multiplicity of an eigenvalue, algebraic 183 Multiplicity of an eigenvalue, geometric 183 Multipole methods 232 245 326 339 Nested dissection 245 NETLIB 330 Newton — Cotes quadrature formula 289 341 Newton's method 101 231 Nondefective matrix 185—186 Nonnormal matrix 186 258 Nonsingular matrix 7 Normal distribution 96 171 240 Normal equations 81 82 130 137 141 204 Normal matrix 92 173 187 201 Norms 17—24 331 Norms, 1-, 2-, 4-, 18 Norms, equivalence of 37 106 117 Norms, induced 18 Norms, matrix 18 22 Norms, vector 17 Norms, weighted 18 24 294 Normwise analysis 127 334 NullSpace 7 33 Nullspace, computation of 36 Numerical analysis, definition of 321—327 Numerical range 209 O ("big O") 103—106 O( 104 One-to-one function 7 Operation count 58—60 Orthogonal matrix 14 218 Orthogonal polynomials 285—292 341 Orthogonal polynomials approximation problem 288 Orthogonal projector 43—47 56 81 83 129 Orthogonal triangularization 69—70 148 Orthogonal vectors 13 Orthogonality, loss of 66—67 282—283 295 Orthonormal basis 36 Orthonormal vectors 13 Outer product 6 22 24 109 see Overdetermined system 77 Overflow 97 p-Norm 18 Pade approximation 311 341 Panel methods 245 Parallel computer 66 233 Partial differential equations 53 244 248 316—318 332 Partial pivoting 156 160 336 Permutation matrix 34 157 220 Pivot element 155 Pivoting in Gaussian elimination 155— 162 336 Polar decomposition 331 Polynomial 4 101 181 283 Polynomial of a matrix 259 265 318 Polynomial, approximation 246 258 268—269 298—299 340—341 Polynomial, Chebyshev 292 300 Polynomial, interpolation 78 96 292 Polynomial, Legendre 53 54 64 68 285—292 Polynomial, monic 183 259 Polynomial, orthogonal 285—292 Polynomial, preconditioner 318 Polynomial, quintic 192 Polynomial, roots 92 101 110 190 191 227 338 Positive definite matrix see "Hermitian positive definite matrix" Potential theory 279 283—284 341 Power iteration 191 204—206 Powers of a matrix 33 120 182 189 PRECISION 98 Preconditioning 274 297 313—319 326 342 Principal minors 154 214 Problem, formal definition 89 102 Problem, instance 89 Problem-solving environment 63 Projector 41 331—332 Projector, complementary 42 Projector, oblique 41 Projector, orthogonal 43—47 56 81 83 129 Projector, rank-one 14 46 Pseudo-minimal polynomial 261 Pseudoinverse 81—85 94 129 335 Pseudospectra 201 265 338 340 Pseudospectra, computation of 201 265 340 Pythagorean Theorem 15 81 Q portrait 169—170 QMR (quasi-minimal residuals) 310—311 341 QR algorithm 211—224 239 253—254 338 QR factorization x 36 48—55 48—55 83 253 332 QR factorization, full 49 QR factorization, reduced 49 QR factorization, with column pivoting 49 143 Quadrature 285—292 Quasi-minimal residuals see "QMR" RADIX 98 random matrix 96 114 167—171 189 233 240 244 262 271 334 Random matrix, orthogonal 65 114 120 Random matrix, sparse 300 309 Random matrix, triangular 96 128 167 RANGE 6 33 Range, computation of 36 Range, sensitivity to perturbations 133—134 Rank 7 33 55 Rank, computation of 36 Rank-deficient matrix 84 143 Rank-one matrix 35 see Rank-one perturbation 16 230 Rank-one projector 14 46 Rank-revealing factorization 336 Rank-two perturbation 232 Rayleigh quotient 203 209 217 254 283 Rayleigh quotient, iteration 207—209 221 338 Rayleigh quotient, shift 221 342 Rayleigh — Ritz procedure 254 Recursion 16 230 249 Reflection 15 29 see Reflection, of light 136 Regression 136 Regularization 36 Residual 77 116 Resolvent 201 Resonance 182 Richardson iteration 274 302 Ritz matrix 276 Ritz values 255 257 278 Rootfinding see "Polynomial roots" Rotation 15 29 31 see Rounding 99 Rounding, errors 321—327 Row, rank 7 Row, vector 21 Schur complement 154 Schur factorization 187 193 337 Secular equation 231 Self-adjoint operator 258 Shadowing 335 Shifts in QR algorithm 212 219—224 Similar matrices 184 Similarity transformation 34 184 Simultaneous inverse iteration 219 Simultaneous iteration 213—218 253—254 Singular value 8 26 Singular value decomposition see "SVD" Singular vector 26 Skeel, condition number 334 Skeel, Robert D. 326 Skew-Hermitian matrix 16 187 Software 330 SOR (successive over-relaxation) 318 339 Sparse, direct methods 339 Sparse, matrix 232 244 300—301 Spectral abscissa 189 258 Spectral methods 53 255 317 326 332 Spectral radius 24 189 Spectrum 181 201 Splitting 317—318 Square root 58 91 127 SSOR (symmetric SOR) 318 Stability 57 66 72 84 89 102—113 326 Stability, formal definition 104 Stability, physical 182 258 Stable algorithm see "Stability" Stationary point 203 283 Steepest descent iteration 302 Stiefel, Eduard 293 341 Strassen's algorithm 247 249 330 340 Sturm sequence 228 SubMatrix 9 333 Subtraction 91 108 Superellipse 18 SVD (singular value decomposition) 25—37 83 113 120 142 201 322 331 SVD (singular value decomposition), computation of 36 113 234—240 339 SVD (singular value decomposition), full 28 SVD (singular value decomposition), reduced 27 Symbolic computation 101 324 Symmetric matrix 11 172 TFQMR (transpose-free QMR) 311 341 Three-step bidiagonalization 238—240 Three-term recurrence relation 229 276 282 287 291 Threshold pivoting 336 Tilde ( 103 Toeplitz matrix 68 318 337 342 Trace 23 Translation-invariance 261 269 TRANSPOSE 11 Transpose-free iterations 311 Traub, Joseph 327 Triangle inequality 17 Triangular matrix 10 15 49 240 triangular" Triangular orthogonalization 51 70 148 Triangular system of equations 54 82—83 117 121—128 Triangular triangularization 148 Tridiagonal biorthogonalization 305—306 Tridiagonal matrix 194 218 Tridiagonal orthogonalization 305—306 Tridiagonal reduction 194 196—201 212 Turing, Alan 325 333 335 342 Underdetermined system 143 Underflow 97 Unit, ball 20 Unit, sphere 25 Unit, triangular matrix 62 148 Unitarily diagonalizable matrix see "Normal matrix" Unitary, diagonalization 187—188 Unitary, equivalence 31 Unitary, matrix 14—16 119 163 187 Unitary, triangularization 188 Unstable algorithm see "Stability" Vandermonde matrix 4 53 64 78 137 289 292 337 von Neumann, John 325 335 336 Wavelets 245 Weighted norm 18 24 294 Well-conditioned matrix 94 Well-conditioned problem 89 91 Wilkinson, James H. 115 325 330 335 336 Wilkinson, James H., book by 331 337 Wilkinson, James H., polynomial 92 Wilkinson, James H., shift 222 224 Zerofinding see "Polynomial roots" Ziggurat 75 \ operator in Matlab 85 138 177 337 ~ 59
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