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Mathews J.H., Fink K.D. — Numerical Methods Using MATLAB
Mathews J.H., Fink K.D. — Numerical Methods Using MATLAB

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Название: Numerical Methods Using MATLAB

Авторы: 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: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1999

Количество страниц: 662

Добавлена в каталог: 25.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$O(h^n)$      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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