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Conte S.D., de Boor C. Elementary numerical analysis - an algorithmic approach
Conte S.D., de Boor C.  Elementary numerical analysis - an algorithmic approach









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: Elementary numerical analysis - an algorithmic approach

: Conte S.D., de Boor C.

: en

: / / /

:

ed2k: ed2k stats

: third edition

: 1980

: 432

: 20.02.2005

: | | ID
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Acceleration      95ff. (See also Extrapolation to the limit)
Adams Bashforth method      373376
Adams Bashforth method, predictor form      383
Adams Bashforth method, program      377
Adams Bashforth method, stability of      392394
Adams Moulton method      382388
Adams Moulton method for systems      399
Adams Moulton method, program      387
Adams Moulton method, stability of      394
Adaptive quadrature      328ff.
Aitkens $D^2$-process      98 196 333
Aitkens $D^2$-process, algorithm      98
Aitkens algorithm for polynomial interpolation      50
Aliasing      273
Alternation in sign      237
Analytic substitution      294ff 339
Angular frequency      271
Approximation      235ff.
Approximation, Chebyshev      235244
Approximation, least-squares      see Least-squares approximation
Approximation, uniform      235244
Back-substitution      148 156 163
Back-substitution, algorithm      148. 163
Back-substitution, program      164
Backward error analysis      911 19 160 179181
Base of a number system      14
Basis for n-vectors      140 141 196
Bessel interpolation      288
Bessels function, zeros of      124125 127
Binary search      87
Binary system      13
Binomial coefficient      57
Binomial function      57 373
Binomial theorem      58
Bisection method      7475 8
Bisection method, algorithm      75
Bisection method, program      8 184
Boundary value problems      406419
Boundary value problems, collocation method for      416419
Boundary value problems, finite difference methods for      406412
Boundary value problems, second-order equation      407ff.
Boundary value problems, shooting methods for      412416
Breakpoints of a piecewise-polynomial function      284 319
Broken-line interpolation      284285
Broydens method      222
Central-difference formula      298 407
Chain rule      28
Characteristic equation of a difference equation      350 391
Characteristic equation of a differential equation      348 392 394
Characteristic equation of a matrix      201
Characteristic polynomial of a matrix      202
Chebyshev approximation      see Approximation uniform
Chebyshev points      54 242244 3
Chebyshev polynomials      32 239241 255256 293 317 354
Chebyshev polynomials, nested multiplication for      258
Choleskis method      160 169
Chopping      8
Compact schemes      160 169
Composite rales for numerical integration      319ff.
Condition      1415
Condition number      175 177
Continuation method      218
Convergence acceleration      95ff. (See also Extrapolation to the limit)
Convergence of a sequence      19ff
Convergence of a vector sequence      191 223
Convergence, geometric      22
Convergence, linear      95
Convergence, order of      102
Convergence, quadratic      100ff
Conversion, binary to decimal      2 6 113
Conversion, decimal to binary      3 6
Corrected trapezoid rale      309 310 321 323
Corrected trapezoid rale, program      324
Corrector formulas      379388
Corrector formulas, Adams Moulton      382384
Corrector formulas, Milnes      385
Cramers rale      144 187
Critical point      209
Cubic spline      289 302
Cubic spline, interpolation      289293
Damped Newtons method      219220
Damping for convergence encouragement      219
Data fitting      245ff.
Decimal system      1
Deflation      117119 124 203
Deflation for power method      207
Degree of polynomial      29 32
Descartes rale of sign      110111 119
Descent direction      213
Determinants      144 185ff 201ff
Diagonally dominant      see Matrix
Difference equations      349ff 360 361 390 391 392
Difference equations, initial value      351
Difference equations, linear      349
Difference operators      61
Differential equations      346ff
Differential equations, basic notions      346348
Differential equations, boundary value problems      406419
Differential equations, Eulers method      356ff.
Differential equations, initial value problems      347 354
Differential equations, linear, with constant coefficients      347349
Differential equations, multistep methods      373ff.
Differential equations, Runge Kutta methods      362ff.
Differential equations, stiff      401ff.
Differential equations, systems of      398401
Differential equations, Taylors algorithm      354359
Differential remainder for Taylors formula      28
Differentiation, Numerical      290 295303
Differentiation, symbolic      356
Direct methods for solving linear systems      147185 209
Discrete Fourier Transform      278
Discretization error      300 359 361 389
Dist      236
Divided difference      40 41ff 62ff 79 236
Divided difference, table      41ff.
DOUBLE PRECISION      7 11 18
Double precision, accumulation      396
Double precision, accumulation of scalar products      183
Double precision, accumulation, partial      3
DVERK subroutine for differential equations      370372 400401
Eigenvalues      189ff.
Eigenvalues, program for      194
Eigenvectors      189 191 194
Eigenvectors, complete set of      1
EISPACK      422
Equivalence of linear systems      149
Error      12ff.
Eulers formula      30 269
Eulers method      356 359362 373 379 395
Exactness of a rale      311
Exponent of a floating-point number      7
Exponential growth      390 391
Extrapolation      54
Extrapolation to the limit      333ff 366 410
Extrapolation to the limit, algorithm      338339 (See also Aitkens $D^2$-process)
Factorization of a matrix      160166 169 187 229
False position method      see Regula falsi
Fast Fourier Transform      277284
Fast Fourier transform, program      281282
Finite-difference methods      406411
Fixed point      88
Fixed-point iteration      79 8899 108 223ff 381
Fixed-point iteration for linear systems      224232
Fixed-point iteration for linear systems, algorithm      227
Fixed-point iteration for systems      223234
Fixed-point iteration, algorithm      89
Floating-point arithmetic      7ff.
Forward difference, formula      297
Forward difference, operator D      56ff 373
Forward difference, table      5861
Forward-shift operator      57
Fourier coefficients      269
Fourier series      269ff.
Fourier transform, discrete      278
Fourier transform, fast      277284
Fraction, binary      5
Fraction, decimal      4
Fractional part of a number      4
Fundamental theorem of algebra      29 202
Gauss elimination      145 149ff.
Gauss elimination for tridiagonal systems      153156
Gauss elimination for tridiagonal systems, program      155
Gauss elimination, algorithm      152153
Gauss elimination, program      164166
Gauss Seidel iteration      230232 234 412
Gauss Seidel iteration, algorithm      230
Gaussian rales for numerical integration      311319 325327
Geometric series      22
Gershgorins disks      200
Gradient      209
Gram Schmidt algorithm      250
Hermite interpolation      286
Hermite polynomials      256 318
Hessenberg matrix      197
Homers method      see Nested multiplication
Homogeneous difference equation      350352
Homogeneous differential equation      347348
Homogeneous linear system      135140
Householder reflections      197
Ill-conditioned      181 249
IMSL (International Mathematical and Statistical Library)      370 421
Initial-value problem      347
Initial-value problem, numerical solution of      354405
Inner product      see Scalar product
Instability      1517 117 376 385 389394 402
Integral part of a number      4
Integral remainder for Taylors formula      27
Integration      303345
Integration, composite rales      309 319ff.
Integration, corrected trapezoid rale      309 321
Integration, Gaussian rales      3113 18
Integration, Gaussian rales, program for weights and nodes      316
Integration, midpoint rale      305 32
Integration, rectangle rale      305 320
Integration, Romberg rale      340345
Integration, Simpsons rale      307 321 385
Integration, trapezoid rale      305 321
Intermediate-value theorem for continuous functions      25 74 89
Interpolating polynomial      3871 295
Interpolating polynomial, difference formula      5562
Interpolating polynomial, error      51ff.
Interpolating polynomial, Lagrange formula      38 3941
Interpolating polynomial, Newton formula      40 41
Interpolating polynomial, uniqueness of      38
Interpolation by polynomials      31ff.
Interpolation by trigonometric polynomials      275276
Interpolation in a function table      4650 5561
Interpolation, broken-line      284285
Interpolation, global      293
Interpolation, iterated linear      50
Interpolation, linear      39
Interpolation, local      293
Interpolation, optimal      276
Interpolation, osculatory      63 67 68 286
Interpolation, quadratic      120 202 213214 416
Interval arithmetic      18
Inverse interpolation      51
Inverse iteration      193195
Inverse of a matrix      133 166
Inverse of a matrix, approximate      225
Inverse of a matrix, calculation of      166168
Inverse of a matrix, program      167
Iterated linear interpolation      50
Iteration function for fixed-point iteration      88 223
Iteration methods for solving linear systems      144 209 223ff.
Iterative improvement      183184 229
Iterative improvement, algorithm      183
Jacobi iteration      226 229 234
Jacobi polynomials      317
Jacobian (matrix)      214 216 404
Kronecker symbol $\delta_{ij}$      201
Lagrange form      38
Lagrange formula for interpolating polynomial      39 295 312
Lagrange polynomials      38 147 259 275 295
Laguerre polynomials      256 318
Least-squares approximation      166 215 247251 259267
Least-squares approximation by polynomials      259ff 302
Least-squares approximation by polynomials, program      263264
Least-squares approximation by trigonometric polynomials      275
Lebesque function      243 244
Legendre polynomials      255 259 260 315
Leibniz formula for divided difference of a product      71
Level line      212
Line search      213214 215
linear combination      134 347
Linear convergence      95 98
Linear independence      140 347 417
Linear operation      294
Linear system      128 136 144
Linear system, numerical solution of      147ff
LINPACK      422
Local discretization error      355 359
Loss of significance      1214 32 116 121 265 300
Lower bound for $dist_x(f,\pi_n)$      236237 245
Lower-triangular      13 1
Maehlys method      119
Mantissa of a floating-point number      7
Matrix      129ff
Matrix, addition      133
Matrix, approximate inverse      225
Matrix, bandtype of banded      350
Matrix, conjugate transposed      142
Matrix, dense      145
Matrix, diagonal      131
Matrix, diagonally dominant      184 201 217 225 230 231. 250 289
Matrix, equality      129
Matrix, general properties      128144
Matrix, hermitian      142 206
Matrix, Hessenberg      197
Matrix, Householder reflection      197
Matrix, identity      132
Matrix, inverse      133 166168
Matrix, invertible      132 152 168 178 185 188 229
Matrix, multiplication      130
Matrix, norm      172
Matrix, null      134
Matrix, permutation      143 186
Matrix, positive definite      159 169 231
Matrix, similar      196
Matrix, sparse      145 231
Matrix, square      129 135
Matrix, symmetric      141 198 206
Matrix, trace      146
Matrix, transpose      141
Matrix, triangular      131 147 168 178 186 234
Matrix, triangular factorization      160166
Matrix, tridiagonal      153156 168 188 198 204206 217 230
Matrix, unitary      197
Matrix-updating methods for solving systems of equations      221222
Mean-value theorem for derivatives      26 52 79 92 96 102 298 360
Mean-value theorem for integrals      26. 304 314 320
Midpoint rule      305
Midpoint rule, composite      321 341
Miillers method      120ff 202204
Milnes method      378 385 389
Minimax approximation      see Approximation uniform
Minor of a matrix      188
Modified regula falsi      77 78 8486 205
Modified regula falsi, algorithm      77
Modified regula falsi, program      8486
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