Авторизация
Поиск по указателям
Kincaid D., Cheney W. — Numerical analysis: mathematics of scientific computing
Обсудите книгу на научном форуме Нашли опечатку?
Название: Numerical analysis: mathematics of scientific computingАвторы: Kincaid D., Cheney W. Аннотация: This book has evolved over many years from lecture notes that accompany cer-
Язык: Рубрика: Математика /Численные методы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1991Количество страниц: 690Добавлена в каталог: 15.07.2005Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
34 219 33—35 162 168 162 192 162 168 10 12 628 457 459 a posteriori bounds 219 A-orthogonal 209 A-orthonormality 208 A-stability 569 Absolute error 41 Adams — Bashforth formula, fifth-order 509 Adams — Bashforth formula, fourth-order 514 Adams — Bashforth — Moulton, systems 529 Adams — Moulton formula, fifth- order 510 Adams — Moulton formula, fourth-order 514 Adaptive approximation 424 Adaptive quadrature 471 Adaptive quadrature, algorithm 475 Adaptive Runge — Kutta — Fehlberg, algorithm 505 Adaptive Runge — Kutta — Fehlberg, method 503 Aitken acceleration 231 Algorithm, see Pseudocode Aliasing 421 422 Antidifferentiation 443 Applications of B-splines 343 Approximate inverse 175 Approximating functions 278 Approximation formula, 433 Approximation formula, 433 Approximation sense of Sard 477 Associated matrix norm 163 Attraction, basin of 105 Autonomous 528 555 570 B-splines applications 343 B-splines, degree 0, 333 B-splines, degree 1, 334 Back substitution 127 145 Back substitution, permuted system 128 Backward SOR 194 Badly conditioned problems 48 Bairstow’s method 96 Bairstow’s method, algorithm 98 Barycentric interpolation formula 295 Basic feasible point 654 Basic functions 552 Basic Gaussian elimination 139 Basic vectors 551 Basin of attraction 105 Bernoulli numbers 358 468 Bernstein polynomials 289 Bessel functions 25 27 53 55 Bessel’s inequality 364 Best approximation 359 Big 10 Binary system 28 Binomial coefficient 289 Birkhoff interpolation 307 Bisection method 57 Bisection method, algorithm 59 Bisection theorem 61 Boolean sum 387 Boundary-value problems 531 540 547 551 Bounded sequence 25 Boundedness 14 Branches 16 Canonical form 614 Carath 375 Cardinal functions 282 435 Cardinal property 386 Cartesian grid 385 Cartesian product 385 Cauchy criterion 82 172 Cauchy — Schwarz inequality 103 478 Chain rule 492 Change of intervals 449 Characteristic curves 598 599 606 614 Characteristic equation 187 228 Characteristic polynomial 21 228 557 Characteristics 606 Characteristics, alternative approach 613 Characterizing best approximations 372 Chebyshev acceleration 197 Chebyshev algorithm 201 Chebyshev Alternation Theorem 288 380 Chebyshev polynomial of the second kind 451 Chebyshev polynomials 285 366 Chebyshev solution of linear equations 376 Chebyshev theory 370 Chebyshev’s quadrature formulas 456 Cholesky factorization 130 133 154 Cholesky factorization, algorithm 134 Choosing nodes 287 Chopped to 6 Chopping 31 Classification, partial differential equations 607 Coarse grid 623 Coarse grid, correction scheme 628 Collocation 551 592 Column equilibration 177 Companion matrix 276 Complex Fourier series 410 Complex Newton’s method 105 Composite rule 445 Computer arithmetic 28 Condition number 51 52 165 Conditioning 51 conjugate 96 191 226 Conjugate direction methods 208 Conjugate gradient method 204 210 Conjugate gradient method, algorithm 210 Conjugate transpose 192 227 237 Consistent 517 636 Consistent systems 644 Continuation methods 108 Continued fractions 403 continuous 2 Continuous functions 13 contours 207 Contractive function/mapping 81 Contractive mapping theorem 82 Convergence 549 Convergence of interpolating polynomials 287 Convergence, linear 12 Convergence, order of 85 Convergence, quadratic 12 Convergence, sequences 9—11 Convergence, superlinear 12 Convergent method 517 Conversion of series to continued fractions 405 Convex 374 Convex combinations 374 Convex hull 374 638 Convexity 374 636 Cosine integral 357 Cramer’s Rule 303 Crank — Nicolson method 582 Critical set, crit ( 372 Crout’s factorization 130 Cube roots of unity 105 Cubic 552 Cubic splines 317 Curvature 322 Damping of errors 625 Decimal system 28 Defective matrix 235 Deflation 92 239 274 Derivative 2 Derivatives, 337 Deviation 359 Deviation array 425 Diagonal structure 126 Diagonalizable matrices 558 Diagonally dominant 152 319 Difference equations 20 22 50 Differentiable 2 Differentiation via polynomial interpolation 434 Diffusion equation 572 Dilogarithm function 357 497 Direct method for computing eigenvalues 228 Direct methods 181 Direction vector 207 Dirichlet problem 586 592 Discrete problem 587 Displacement operator 21 Distance from a function to a spline space 352 Divided differences 296 298 Divided differences with repetitions 311 Divided-difference properties 301 Doolittle’s factorization 130 Doolittle’s factorization, algorithm 131 Double-precision 30 Dual problem 649 Duality theory 649 Eigenvalue 187 227 555 Eigenvalue problem 226 Eigenvector 227 555 Elementary matrix 120 Elementary operations 118 Elementary row and column operations 275 Elliptic integral 497 Elliptic integral, second kind 496 Elliptic partial differential equations 607 Embedded Runge — Kutta procedures 505 Entire function 288 Equilibration 176 Equivalent systems 118 140 Error analysis 460 619 Error analysis, bisection method 61 Error analysis, functional iteration 84 Error analysis, Gaussian quadrature 460 Error analysis, Newton’s method 66 Error analysis, secant method 76 Error function, erf(x) 15 356 495 Error in polynomial interpolation 284 Error vector 166 174 Errors 494 502 583 Euclidean norm 162 192 227 Euler — Maclaurin formula 468 484 Euler’s formula 410 Euler’s method 113 495 566 Evaluation of functions 45 51 Excess in row 160 Exchange 383 Exchange method 382 Explicit functions 15 Explicit method 511 517 572 575 EXPONENT 29 Exponential integrals 54 Exponential polynomial 413 422 Extended-precision 30 Extrapolation 194 Extreme point 639 Extremum problem 359 Factor Theorem 89 Factorization phase 145 Factorization phase, algorithm 148 Factorizations 129 Factorizations 149 Farkas Theorem 643 Fast Fourier sine transformation 632 Fast Fourier Transform 409 414 Fast Fourier transform, algorithm 419 Fast methods for Poisson’s equation 631 Feasible point 113 648 Feasible set 113 648 652 Fibonacci sequence 19 54 Finite-difference method 547 574 586 Finite-element method 597 First-degree spline 424 First-order partial differential equations 598 First-variational equation 543 Fixed point 81 Floating-point arithmetic 31 Floating-point error analysis 35 floating-point numbers 28 Forward elimination 145 Forward SOR 194 Forward substitution 127 Forward substitution, permuted system 128 Fourier method 578 Fourier series 410 Fractal 106 Fresnel integral 357 496 Frobenius norm 169 Full pivoting 156 Fully implicit method 581 Functional iteration 80 511 Fundamental matrix 562 Fundamental polynomials for interpolation 444 Fundamental theorem of algebra 89 226 Galerkin method 591 620 Gauss — Jordan method 161 Gauss — Seidel method 182 189 589 624 629 Gaussian elimination, scaled row pivoting 145 Gaussian quadrature 456 Generalized eigenvalue problem 276 Generalized Pythagorean law 364 Gerschgorin’s theorem 240 Global errors 516 Global roundoff error 494 Global truncation error 494 520 Gram matrix 368 Gram — Schmidt process 246 365 Gram — Schmidt process, algorithm 247 Greatest lower bound, glb 14—15 Green’s function 536 537 Grid correction 627 Haar subspace 378 Hailey’s method 74 Half-space 642 Harmonic 592 Harmonic series 47 Heat equation 572 607 Hermite interpolation 305 Hermite’s quadrature formula 456 Hermitian 192 238 Hessenberg matrix 270 Heun’s method 500 Higher transcendental functions 355 Higher-degree natural spline 324 Higher-order divided differences 298 Higher-order ordinary differential equations 524 Hilbert matrix 53 369 Homotopy 108 Horner’s algorithm, complete 93 Horner’s method 14 Horner’s method, algorithm 41 91 280 Householder factorization 251 253 Householder transformations 251 Hyperbolic partial differential equations 607 Hyperbolic problems 616 Idempotent 267 Identity matrix 119 Ill-conditioned 51 52 167 283 Implicit function theorem 16 Implicit functions 15 68 Implicit method 512 571 580
Реклама
-norm 
-norm 
-norm 
-notation 
-cycle algorithm 
-orthogonal 
, functions and sequences 
odory’s Theorem 
-digit approximation 
) 
-splines 
|
|
О проекте