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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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Предметный указатель
Minimum, golden ratio search 401 412 Minimum, gradient method 412 420 Minimum, Nelder — Mead 405 414 Modified Euler method 465 Muller’s method 92 97 Multiple root 75 82 87 #23) Multistep methods, Adams — Bashforth — Moulton method 474 Multistep methods, Hamming’s method 484 Multistep methods, Milne — Simpson method 477 Multistep methods, Natural cubic splines 284 285 Near-minimax approximation 231 233 238 Nelder — Mead 405 414 Nested multiplication 10 221 Neumann boundary conditions 541 545 Newton divided differences 223 Newton polynomial 220 224 227 Newton systems 176 179 Newton — Cotes formulas 344 Newton — Raphson formula 82 84 88 176 179 Newton’s method, multiple roots 75 82 87 #23) Newton’s method, order of convergence 77 nodes 203 207 211 213 234 344 389 Norm, Euclidean 103 162 163 Norm, matrix 566 Normal equations 255 Numerical differentiation 313 314 320 329 333 Numerical differentiation, backward differences 334 Numerical differentiation, central differences 313 314 329 340 #8) Numerical differentiation, error formula 313 314 316 318 Numerical differentiation, forward differences 334 341 Numerical differentiation, higher derivatives 329 333 Numerical differentiation, Richardson extrapolation 320 Numerical integration, adaptive quadrature 382 387 Numerical integration, Boole’s rule 344 372 375 380 #4) 389 Numerical integration, composite rules 350 354 358 363 Numerical integration, cubic splines 296 (#12) Numerical integration, Gauss — Legendre integration 389 392 394 Numerical integration, midpoint rule 366 (#12) 381 Numerical integration, Newton — Cotes 344 Numerical integration, Romberg integration 373 375 377 378 381 Numerical integration, Simpson’s rule 344 353 354 359 363 370 380 387 Numerical integration, Trapezoidal rule 344 354 358 363 368 377 Odd function 301 Optimization, golden ratio search 401 412 Optimization, gradient method 412 420 Optimization, Nelder — Mead 405 414 Optimum step size, differential equations 466 476 479 Optimum step size, differentiation 316 317 Optimum step size, integration 358 382 Optimum step size, interpolation 213 234 Order of approximation 29 32 214 313 329 333 373 377 Order of convergence 32 75 Orthogonal polynomials, Chebyshev 238 Pade approximation 243 246 Parabolic equation 526 Partial derivative 517 527 538 Partial differential equations 514 516 526 538 Partial differential equations, elliptic equations 538 Partial differential equations, hyperbolic equations 516 Partial differential equations, parabolic equations 526 Partial pivoting 133 Periodic function 298 Piecewise, continuous 298 Piecewise, cubic 281 Piecewise, linear 280 Pivoting, element 127 Pivoting, row 127 Pivoting, strategies 131 133 Plane rotations 115 581 Poisson’s equation 538 548 Polynomials, calculus 204 Polynomials, characteristic 559 Polynomials, Chebyshev 230 233 238 240 Polynomials, derivative 204 334 336 Polynomials, interpolation 204 207 210 211 217 224 227 238 Polynomials, Lagrange 207 211 236 Polynomials, Newton 22:0 224 227 Polynomials, Taylor 8 26 31 189 Polynomials, trigonometric 297 303 306 Polynomials, wiggle 273 Power method 568 570 573 576 Predator-prey model 495 (#13) Predictor-corrector method 474 Projectile motion 73 442 450 Propagation of error 32 QR method 606 Quadratic convergence 76 77 82 87 #23) Quadratic formula 39 (#12) Quadrature, adaptive quadrature 382 387 Quadrature, Boole’s rule 344 372 375 380 #4) 389 Quadrature, composite rales 350 354 358 363 Quadrature, cubic splines 296 (#12) Quadrature, Gauss — Legendre integration 389 392 394 Quadrature, midpoint rule 366 (#12) 381 Quadrature, Newton — Cotes 344 Quadrature, Romberg integration 373 375 377 378 381 Quadrature, Simpson’s rule 344 353 354 359 363 370 380 387 Quadrature, Trapezoidal rule 344 354 358 363 368 377 Radioactive decay 432 (#17) Rational function 243 Regula falsi method 56 60 Relative error 24 66 Residual 167 (#5) 253 Richardson, differential equations 449 (#7) 456 471 Richardson, numerical differentiation 320 322 Richardson, numerical integration 375 Rolle’s Theorem 5 6 198 212 219 Romberg integration 373 375 377 378 381 Root finding, bisection 53 54 59 Root finding, Muller 92 97 Root finding, multiple roots 75 82 87 #23) Root finding, Newton 82 84 88 176 179 Root finding, quadratic function 39 (#12) Root finding, regula falsi 56 60 Root finding, secant 80. 84 87 Root finding, Steffensen 92 95 Root of equation 53 75 Root, location 68 Root, multiple 75 82 87 #23) Root, simple 75 77 87 Root, synthetic division 10 200 Root-mean-square error 253 Rotation 115 581 Rounding error 27 Rounding error, differentiation 313 314 316 318 Rounding error, floating point number 21 Row operations 127 Runge phenomenon 236 Runge — Kutta methods 458 461 466 468 488 502 Runge — Kutta methods, Fehlberg method 466 469 Runge — Kutta methods, Richardson extrapolation 471 (#7) Runge — Kutta methods, systems 488 Scaled partial pivoting 133 schur 563 Scientific notation 19 Secant method 80 84 87 Seidel iteration 174 179 SEQUENCE 3 41 Sequence, convergent 3 Sequence, error 3 Sequence, geometric 16 51 Sequential integration, Boole 372 375 Sequential integration, Simpson 370 375 Sequential integration, trapezoidal 369 375 377 Series, binomial 196 (#10) Series, convergence 8 99 189 194 Series, geometric 16 51 Series, Maclaurin 243 Series, Taylor 8 26 31 189 313 329 Shooting method 498 503 Significant digits 25 Similarity transformation 582 Simple root 75 77 87 Simpson’s rule 344 353 354 359 363 370 387 Simpson’s rule, three-eighths rule 344 353 380 Single precision 22 Single-step methods 474 Slope methods 70 80 84 SOR method 545 Spectral radius theorem 566 Splines end constraints 284 Splines, clamped 284 285 293 Splines, integrating 296 (#12) Splines, linear 280 Splines, natural 284 285 Square-root algorithm 72 Stability of differential equations 478 481 Steepest descent 412 420 Steffensen’s method 92 95 Step size, differential equations 466 476 479 Step size, differentiation 316 318 Step size, integration 358 382 Step size, interpolation 213 234 Stopping criteria 58 62 Successive over-relaxation 545 Surface area 364 (#3) Synthetic division 10 200 Systems, differential 487 Systems, linear 114 121. 128 136 143 150 156 163 Systems, nonlinear 167 174 Taylor series 8 26 31 189 313 329 Taylor’s method 451 452 Termination criterion, bisection method 58 Termination criterion, Newton’s method 84 Termination criterion, regula falsi method 58 60 Termination criterion, Romberg integration 378 Termination criterion, Runge — Kutta method 469 Termination criterion, secant method 84 Transformation, elementary 125 Trapezoidal rule 344 354 358 363 369 377 Triangular factorization 141 143 149 Trigonometric polynomials 297 303 306 Truncation error 26 313 314 Unimodal function 402 Unstable error 33 Upper-triangularization 136 150 Vectors, dot product 103 Vectors, Euclidean norm 103 162 163 Wave equation 516 519 Weights, for integration rules 344 393 Wiggle 273 Zeros of Chebyshev polynomials 232 Zeros of functions 53 75 Zeros, root finding 40 51 70 90 167 174
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