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Mathews J.H., Fink K.D. — Numerical Methods Using MATLAB
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Название: Numerical Methods Using MATLABАвторы: Mathews J.H., Fink K.D. Аннотация: Provides an introduction to numerical analysis for undergraduates in mathematics, computer science, physical sciences, and engineering. Emphasis is on why numerical methods work and their limitations, with material balanced between theory, error analysis, and readability. MATLAB programs are the vehicle for presenting underlying numerical algorithms. Includes exercises and computer assignments, with extensive use of MATLAB, new to this third edition. Assumes previous courses in calculus and structured programming. Book News, Inc.®, Portland, OR
Язык: Рубрика: Математика /Численные методы /Численный анализ /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: third editionГод издания: 1999Количество страниц: 662Добавлена в каталог: 25.02.2005Операции: Положить на полку |
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29 32 214 313 314 329 333 373 377 437 445 452 461 475.477 Accelerating convergence, Aitken’s process 90 99 Accelerating convergence, Newton — Raphson 71 82 88 176 Accelerating convergence, Steffensen’s method 90 95 Adam — Bashforth — Moulton method 474 482 Adaptive quadrature 382 387 Aitken’s process 90 99 Approximate significant digils 25 Approximation of data, least-squares curves 211 257 Approximation of data, least-squares line 255 258 Approximation of data, least-squares polynomial 271 274 Approximation of functions, Chebyshev polynomial 230 233 238 240 Approximation of functions, Lagrange polynomial 207 211 213 217 238 Approximation of functions, least squares 255 257 271 Approximation of functions, Newton polynomial 220 224 227 Approximation of functions, Pade approximation 243 246 Approximation of functions, rational functions 243 Approximation of functions, splines 280 281 285 293 Approximation of functions, Taylor polymomials 8 26 31 189 Augmented matrix 126 129 Back substitution 121 123 136 Backward difference 334 Basis 557 Binary numbers 13 17 19 Binomial series 197 (#14) Bisection method 53 54 59 Bolzano’s method 53 Boole’s rule 344 372 375 380 #4) 389 Boundary value problems 497 503 505 510 Bracketing methods 51 53 Central difference 313 314 329 340 #8) Characteristic polynomial 559 Chebyshev nodes 232 Chebyshev polynomial, interpolation 230 233 238 240 Chebyshev polynomial, minimization 233 Chebyshev polynomial, nodes 234 Chopped number 27 Composite Simpson’s rule 350 354 359 363 Composite trapezoidal rule 350 354 358 363 Computer accuracy 21 Continuous function 3 Convergence, acceleration 82 87 90 92 95 Convergence, criteria 62 66 Convergence, global (local) 62 Convergence, linear 76 77 90 Convergence, Newton — Raphson 77 82 87 #23) Convergence, order of 32 75 Convergence, quadratic 76 77 82 87 #23) Convergence, sequence 3 Convergence, series 8 99 Convergence, speed 75 Corrector formula 475 477 Crank — Nicholson method 531 535 Cube-root algorithm 86 (#11) Cubic spline, clamped 284 285 293 Cubic spline, natural 284 285 Deflation of eigenvalues 578 Derivative, definition 5 311 Derivative, formulas 204 313 322 329 333 505 Derivative, higher 329 333 505 Derivative, partial 325 (#7) 517 527 538 Derivative, polynomials 204 334 336 Determinant 113 114 123 151 Difference equation 505 517 527 531 539 Difference, backward 334 Difference, central 313 314 329 340 #8) Difference, divided 223 Difference, finite-difference method 505 510 514 Difference, forward 334 341 Difference, table 224 Differential equation, Adams — Bashforth — Moulton method 474 482 Differential equation, boundary value problems 497 503 505 510 Differential equation, Crank — Nicholson method 531 535 Differential equation, Dirichlet method for Laplace’s equation 549 Differential equation, Euler’s method 433 437 440 Differential equation, existence-uniqueness 430 Differential equation, finite-difference method 505 510 514 517 527 539 Differential equation, forward-difference method 528 533 Differential equation, Hamming’s method 484 Differential equation, Heun’s method 443 445 448 465 Differential equation, higher-order equations 490 Differential equation, initial value problem 428 430 487 498 Differential equation, Milne — Simpson method 477 Differential equation, modified Euler method 465 Differential equation, partial differential equations 514 516 526 538 Differential equation, predictor 474 477 Differential equation, Runge — Ktitta — Fehlberg method 466 469 Differential equation, Runge — Kutta method 458 461 466 468 488 502 Differential equation, shooting method 498 503 Differential equation, stability of solutions 478 481 Differential equation, Taylor methods 451 452 455 Digit, binary 14 17 19 Digit, decimal 14 19 22 Dirichlet method for Laplace’s equation 549 Distance between points 103 162 Divided differences 223 Division by zero 74 77 Division, synthetic 10 200 Dot product 103 DOUBLE PRECISION 22 Double root 75 77 87 d’Alembert’s solution 519 Eigenvalues, characteristic polynomial 559 Eigenvalues, definition 559 Eigenvalues, dominant 568 Eigenvalues, Householder’s method 594 Eigenvalues, inverse power method 573 575 576 Eigenvalues, Jacobi’s. method 581 Eigenvalues, power method 568 570 573 576 Eigenvalues, QR method 601 Eigenvectors, definition 559 Eigenvectors, dominant 568 Elementary row operations 126 Elementary transformations 125 Elliptic equations 538 Endpoint constraints for splines 284 Epidemic model 442 (#9) Equivalent linear systems 125 Error, absolute 24 Error, bound 189 194 Error, computer 21 27 135 Error, data 36 203 316 Error, differential equations 437 445 452 462 475 477 519 Error, differentiation 313 314 316 318 Error, integration 344 358 359 377 Error, interpolating polynomial 189 213 238 Error, loss of significance 28 Error, propagation 32 Error, relative 24 66 Error, root mean square 253 Error, round-off 27 Error, sequence 3 Error, stable (unstable) 33 Error, subtractive cancellation 28 Error, truncation 26 313 314 Euclidean norm 103 162 163 Euler formulas 299 Euler’s method 433 437 440 Euler’s method, global error 437 Euler’s method, modified 465 Euler’s method, systems 488 Even function 300 Exponential fit 263 Extrapolated value 199 extrema 400 404 Extreme Value Theorem 4 False position method 56 60 Final global error 437 445 452 462 Finite difference method! 505 510 514 517 527 539 Fixed-point iteration 42 49 173 Fixed-point iteration, error bound 46 Floating-point number 21 22 Floating-point number, accuracy 21 Forward difference 334 341 Forward difference method 527 528 533 Forward substitution 125 (#2) Fourier series 299 Fourier series, discrete 304 Fractions, binary 17 Fundamental theorem of calculus 6 Gauss — Legendre integration 389 392 394 Gauss — Seidel iteration 159 161 164 Gaussian elimination 125 128 143 150 Gaussian elimination, back substitution 121 123 Gaussian elimination, computational complexity 147 Gaussian elimination, LU factorization 141 143 150 Gaussian elimination, multipliers 127 129 Gaussian elimination, pivoting 127 131 Gaussian elimination, tridiagonal systems 140 (#1) 166 284 506 599 Generalized Rolle’s theorem 6 (#20) Geometric series 16 51 Gerschgorin’s circle theorem 566 Golden ratio search 401 412 Gradient 412 420 Graphical analysis, fixed-point iteration 47 Graphical analysis, Newton’s method 70 78 79 Graphical analysis, secant method 80 Halley’s method 87 (#22) Hamming’s method 484 Heat equation 515 Helmholtz’s equation 538 548 Heun’s method 443 445 448 465 Higher derivatives 329 333 Hilbert matrix 139 (#15) Hooke’s law 262 (#1) Horner’s method 10 200 Householder’s method 594 Hyperbolic equations 516 Ill-conditioning, least-squares data fitting 134 Ill-conditioning, matrices 133 139 Initial value problem 428 430 487 498 Integration, adaptive quadrature 382 387 Integration, Boole’s rule 344 372 375 380 #4) 389 Integration, composite rules 350 354 358 363 Integration, cubic splines 296 (#12) Integration, Gauss — Legendre integration 389 392 394 Integration, midpoint rule 366 (#12) 381 Integration, Newton — Cotes 344 Integration, Romberg integration 373 375 377 378 381 Integration, Simpson’s rule 344 353 354 359 363 370 380 387 Integration, trapezoidal rule 344 354 358 363 368 377 Intermediate Value Theorem 3 Interpolation, Chebyshev polynomials 230 233 238 240 Interpolation, cubic splines 281 285—287 293 Interpolation, error, polynomials 8 31 189 211 213 238 Interpolation, extrapolation 199 Interpolation, integration 296 (#12) 344 Interpolation, Lagrange polynomials 207 211 213 217 238 Interpolation, least squares 255 271 Interpolation, linear 207 219 255 277 280 Interpolation, Newton polynomials 220 224 227 Interpolation, Pade approximations 243 246 Interpolation, piecewise linear 280 Interpolation, polynomial wiggle 273 Interpolation, rational functions 243 Interpolation, Runge phenomenon 236 Interpolation, Taylor polynomials 8 26 31 189 313 329 Interpolation, trigonometric polynomials 297 303 306 Iteration methods, bisection 53 54 59 Iteration methods, fixed point 42 173 544 Iteration methods, Gauss — Seidel 159 161 164 Iteration methods, Jacobi iteration 156 161 163 Iteration methods, Muller 92 97 Iteration methods, Newton 70 82 84 88 176 179 Iteration methods, partial differential equations 546 Iteration methods, regula falsi 56 60 Iteration methods, secant 80 84 87 Iteration methods, Steffensen 92 95 Jacobi iteration for linear systems 156 161 163 Jacobian matrix 170 176 Jacobi’s method for eigenvalues 581 590 Lagrange polynomials 207 211 213 236 Laplace’s equation 538 549 Least-squares data fitting, data linearization 266 Least-squares data fitting, linear fit 255 258 260 277 Least-squares data fitting, nonlinear fit 257 266 271 Least-squares data fitting, plane 277 (#17 #18) Least-squares data fitting, polynomial fit 271 Least-squares data fitting, root-mean-square error 253 Least-squares data fitting, trigonometric polynomials 297 303 306 Length of a curve 364 (#2) Length of a vector 103 162 163 Limit, function 2 Limit, sequence 3 Limit, series 8 Linear approximation 219 (#12) 255 258 277 280 linear combination 103 499 Linear convergence 76 77 Linear independence 557 Linear least-squares fit 255 258 260 277 Linear system 114 121 128 143 152 156 163 Linear systems of equations, back substitution 121 123 136 Linear systems of equations, forward substitution 125 (#2) Linear systems of equations, Gaussian elimination 125 128 143 150 Linear systems of equations, LU factorization 141 143 150 Linear systems of equations, tridiagonal systems 140 (#1) 166 284 506 599 Linear systems, theory, matrix form 111 114 127 141 Linear systems, theory, nonsingular 114 Lipschitz condition 430 Location of roots 68 Logistic rule of population growth 276 (#6 #7) Loss of significance 28 Lower triangular determinant 123 LU factorization 141 143 150 Machine numbers 20 Maclaurin series 243 Mantissa 20 22 Markov process 579 (#5) Matrix, addition 107 Matrix, augmented 126 129 Matrix, determinant 113 114 123 151 Matrix, diagonalization 563 Matrix, eigenvalue 559 Matrix, eigenvector 559 Matrix, equality 106 Matrix, Hilbert 139 (#15) Matrix, identity 112 Matrix, ill-conditioned 133 139 Matrix, inverse 112 114 Matrix, lower triangular 120 125 143 Matrix, LU factorization 141 143 150 Matrix, multiplication 110 112 143 150 Matrix, nonsingular 112 Matrix, norm 566 Matrix, orthogonal 565 594 Matrix, permutation 148 150 Matrix, singular 113 Matrix, strictly diagonally dominant 160 162 163 Matrix, symmetric 109 (#6) 565 581 590 594 Matrix, transpose 104 108 270 Matrix, triangular 120 125 Matrix, tridiagonal 140 (#1) 166 284 506 599 Mean of data 260 (#4 #5 #6) Mean value theorems, derivative 5 45 Mean value theorems, integrals 6 Mean value theorems, intermediate 3 Mean value theorems, weighted integral 7 Midpoint rule 366 (#12) 381 Milne — Simpson method 477 483 Minimax approximation, Chebyshev 231 233 238
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