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Burden R.L., Faires J.D. — Numerical analysis
Burden R.L., Faires J.D. — Numerical analysis

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Название: Numerical analysis

Авторы: Burden R.L., Faires J.D.

Аннотация:

The book contains sufficient material for a full year of study, but we expect many readers to use tbe text for only a single-terra course. In such a course, students learn to identify the type of problems that require numerica) techniques for their solution, see examples of error propagation that can occur when numerical methods are applied, and accurately approximate the solutions of some problems that cannot be solved exactly. The remainder of the text serves as a reference for methods that are not discussed in the course. Either the full-year or single-course treatment is consistent with the purpose of the text.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 5-th edition

Год издания: 1993

Количество страниц: 772

Добавлена в каталог: 27.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$LDL^{t}$ Factorization Algorithm      376
$l_{1}$ norm of a matrix      400
$l_{1}$ norm of a vector      399
$l_{2}$ norm of a matrix      397 403
$l_{2}$ norm of a vector      391
$l_{\infty}$ norm of a matrix      397
$l_{\infty}$ norm of a vector      391
$\pi$, approximating      174
A-stable      317
Absolute deviation      437
Absolute error      15
Absolute stability, region of      317
Accelerating convergence      78
Accuracy, degree of      179
Adams Fourth-Order Predictor-Corrector Algorithm      279
Adams Variable-Step-Size Predictor-Corrector Algorithm      284
Adams — Bashforth method      275
Adams — Moulton method      276
Adaptive Quadrature Algorithm      196
Adaptive quadrature method      192
Aitken's $\Delta^{2}$ method      78 515
Algebraic polynomial      96
Algorithm, description of      24
Algorithm, stable      26
Algorithm, unstable      26
Annihilation technique      521
Annuity      67
Approximating $\pi$      174
Approximation theory      435
Asymptotic error constant      70
Augmented matrix      326
Average value of a function      6
B-splines      613
Backward difference formula      116 158
Backward difference method      639
Backward difference notation      116
Backward error analysis      431
Backward Euler method      321
Backward substitution      325
Band matrix      379
Band width      379
Basis for $\mathbb{R}$      498
Basis functions, B-spline      613
Basis functions, piecewise bilinear      670
Basis functions, piecewise linear      607
Beam deflection problem      577 598 604
Bell-shaped spline      613
Bernoulli equation      270
Bernstein polynomial      111
Bessel function      104
Bezier Curve Algorithm      153
Bezier polynomial      151
Bilinear basis functions      670
Binary digit      13
Binary representation of a number      13
Binary search method      40
Bisection Algorithm      41
Bisection method as a starting procedure      43
Bisection method description      40
Bisection method rate of convergence      43
Bisection method stopping procedure      42
Bit      13
BLAS      36
Block tridiagonal matrix      384
Boundary-value problem definition      578
Boundary-value problem extrapolation      596 602
Boundary-value problem, B-splines      613
Boundary-value problem, centered difference formula      592
Boundary-value problem, collocation method      618
Boundary-value problem, Cubic Spline Rayleigh — Ritz Algorithm      616
Boundary-value problem, finite-difference method      592 598
Boundary-value problem, Galerkin method      618
Boundary-value problem, linear      578 592
Boundary-value problem, Linear Finite-Difference Algorithm      594
Boundary-value problem, Linear Shooting Algorithm      580
Boundary-value problem, nonlinear      585 598
Boundary-value problem, Nonlinear Finite-Difference Algorithm      601
Boundary-value problem, Nonlinear Shooting Algorithm      588
Boundary-value problem, Piecewise Linear Rayleigh — Ritz Algorithm      610
Boundary-value problem, Rayleigh — Ritz method      605
Boundary-value problem, reverse shooting technique      583
Brent method      94
Bridgedruss      389 423
Broyden Algorithm      563
Broyden method      561
Cauchy method      94
Cauchy — Buniakowsky — Schwarz inequality for sums      393
Cautious Romberg method      203 230
Center of mass problem      221
Centered difference formula      118 592
Centered difference method      626
Centered difference operator      121
Characteristic      13
Characteristic multistep method      309
Characteristic polynomial matrix      401
Characteristic value      401 see
Characteristic vector      401 see
Chebyshev economization      466
Chebyshev polynomial      91 459
Chebyshev Rational Approximation Algorithm      476
Choleski Algorithm      376
Choleski method      366
Chopping arithmetic      15
Clamped boundary      133
Clamped Cubic Spline Algorithm      138
Closed method      271 see
Closed Newton — Cotes formula      179
Coaxial cable problem      635
Collocation method      618
Column vector      326
Composite midpoint rule      188
Composite numerical integration      184
Composite Simpson's Algorithm      186
Composite trapezoidal rule      187
Computer arithmetic      12
Computer graphics      150
Condition number definition      426
Condition number, approximating      427
Conditionally stable      638
Consistent multistep method      308
Consistent one-step method      304
Contagious disease problem      269
Continued fraction      474
Continuous function from $\mathbb{R}$ to $\mathbb{R}$      2
Continuous function from $\mathbb{R}^{n}$ to $\mathbb{R}$      546
Continuous function from $\mathbb{R}^{n}$ to $\mathbb{R}^{n}$      547
Contraction mapping theorem      547
Convergence, accelerating      78
Convergence, cubic      77
Convergence, linear      70
Convergence, order of      70
Convergence, quadratic      70
Convergence, rate of      29
Convergence, superlinear      82 561
Convergence, vector      394
Convergent matrix      404
Convergent multistep method      309
Convergent one-step method      304
Convergent sequence      3
Convergent vectors      390
Convex set      234
Cooley — Tukey algorithm      486
Coordinate function      545
Corrugated roofing problem      156 192 204
Cramer's rule      361
Crank — Nicolson Algorithm      644
Crout method      366
Crout Reduction for Tridiagonal Linear Systems Algorithm      380
Cubic convergence      77
Cubic Hermite interpolation      131 150 251
Cubic spline algorithm, clamped      138
Cubic spline algorithm, natural      136
Cubic spline interpolation      132 613
Cubic Spline Rayleigh — Ritz Algorithm      616
Decimal machine number      15
Deflation      86 516
Degree of accuracy      179
Degree of precision      179
Derivative approximation      157
Derivative definition      3
Derivative relative to continuity      4
DERIVE      38
Determinant of a matrix      358
Diagonal matrix      348
Difference backward      116
Difference equation      239
Difference forward      79
Differentiable function      3
Differential equation, approximating      233 578 623
Differential equation, boundary-value problem      see "Boundary-value problem"
Differential equation, initial-value problem      see "Initial-value problem"
Differential equation, perturbed      236
Differential equation, well-posed      236
Differentiation      see "Numerical differentiation"
Diffusion equation      624
Direct Factorization Algorithm      366
Direct factorization of matrices      362
Directional derivative      569
Dirichlet boundary conditions      623
Discrete least-squares      436
Disk brake problem      191
Distance between matrices      396
Distance between vectors      393
Distribution of heat, steady-state      623
Divided difference      112
Doolittle's method      366
Double integral      210
DOUBLE PRECISION      14
Drug concentration problem      67
Economization of power series      466
Eigenvalue definition      401
Eigenvalue, approximating      498
Eigenvalue, bound for      503
Eigenvector definition      401
Eigenvector, linear independence      500
Eigenvector, orthonormal      502
EISPACK      36 541
Electrical circuit problems      167 247 288 297 323
Electrical transmission problem      657
Electrostatic potential problem      584
Elliptic partial-differential equation      623 625
Equal matrices      345
Error function      12 111 205
Error in computer arithmetic      12
Error, absolute      15
Error, control      263 282
Error, exponential growth      26
Error, global      304
Error, linear growth      26
Error, local truncation      248 274 305
Error, relative      15
Error, round-off      15
Error, truncation      8
Escape velocity problem      229
Euclidean norm      391 see
Euler algorithm      240
Euler method      239
Euler modified method      257
Explicit method      179 271
Extended midpoint rule      188 see
Extended Simpson's rule      186 see
Extended trapezoidal rule      187 see
Extrapolation Algorithm      290
Extrapolation, derivative      168
Extrapolation, initial-value problem      288
Extrapolation, integration      199
Extrapolation, linear boundary-value problem      596
Extrapolation, nonlinear boundary-value problem      602
Extreme Value Theorem      5
Factorization of a matrix      362
False position, method of      63
Fast Fourier transform (FFT) algorithm      492
Fast Fourier transform method      486
Fibonacci problem      92
Fibonacci sequence      31
Finite-difference method, linear      592
Finite-difference method, nonlinear      598
Finite-digit arithmetic      15
Finite-Element Algorithm      664
Finite-element method      657
First divided difference      112
Five-point formula      161
Fixed Point Iteration      50 549
Fixed Point Iteration Algorithm      50
Fixed point theorem      52 547
Fixed point, definition of      46 547
Floating-point form      13
Forward difference, formula      158
Forward difference, method      637
Forward difference, notation      79 116
Fourier series      455
Fourth-order Adams — Bashforth technique      271
Fourth-order Adams — Moulton technique      271
Fredholm integral equation      337
Free boundary      133
Frobenius norm of a matrix      400
Function, average value      6
Function, Bessel      104
Function, continuous      2 546
Function, coordinate      545
Function, differentiable      3
Function, limit      2 546
Function, orthogonal      454
Function, orthonormal      454
Function, rational      469
Function, weight      453
Functional iteration      50
Fundamental theorem of algebra      82
Galerkin method      618
Gauss      38
Gauss transformation matrix      363
Gauss — Jordan method      336
Gauss — Seidel Iterative Algorithm      411
Gauss — Seidel iterative method      410
Gauss — Seidel method for nonlinear systems      550
Gaussian Double Integral Algorithm      218
Gaussian Elimination with Backward Substitution Algorithm      330
Gaussian Elimination with Maximal Column Pivoting Algorithm      340
Gaussian Elimination with Scaled-Column Pivoting Algorithm      343
Gaussian elimination, operation count      332
Gaussian quadrature      205 214
Gaussian Triple Integral Algorithm      219
Gaussian — Kronrod method      230
Generalized Rolle's Theorem      7
Gerschgorin Circle Theorem      503
Global error      304
Golden ratio      31
Gompertz population growth      68
Gradient      569
Gragg extrapolation      288
Gram — Schmidt process      456
Graphics, computer      150
Gravity flow discharge problem      559
Grid lines      626
Growth of error, exponential      26
Growth of error, linear      26
Guidepoint      150
Heat distribution, steady state      623
Heat equation      623
Heat Equation Backward-Difference Algorithm      640
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