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Phillips G.M. — Interpolation and Approximation by Polynomials
Phillips G.M. — Interpolation and Approximation by Polynomials

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Название: Interpolation and Approximation by Polynomials

Автор: Phillips G.M.

Аннотация:

This book covers the main topics concerned with interpolation and approximation by polynomials. This subject can be traced back to the precalculus era but has enjoyed most of its growth and development since the end of the nineteenth century and is still a lively and flourishing part of mathematics. In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples, and each section ends with a number of carefully selected problems that extend the student's understanding of the text.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 312

Добавлена в каталог: 13.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Aitken, A.C.      11
Andrews, George E.      299 303
Approximation      see “Best approximation”
B-spline      218
B-spline, cubic      230
B-spline, quadratic      224
B-spline, uniform      229
Back substitution      21
Backward difference formula      37
Banded matrix      276
Barycentric coordinates      191
Basis      163
Berman, D.L.      107
Bernoulli numbers      134
Bernoulli polynomial      135
Bernoulli, Jacob      134
Bernstein operator      248
Bernstein polynomial      247 267
Bernstein theorem      255
Bernstein, S.N.      87 107
Best approximation      57
Blending function      165
Bohman — Korovkin theorem      263 265 266 269
Briggs, Henry      31
Brutman, Lev      vii 101 113
Cartesian product      166
Cauchy — Binet identity      275
Central differences      40
Chebyshev coefficient      71 86
Chebyshev polynomial      65 67
Chebyshev polynomial second kind      65 75
Chebyshev, P.L.      64
Cheney, E.W.      vii 247 263
Chu — Vandermonde identity      298
Chung and Yao      196
Composite rule      125
Convex function      259 269 270
Cotes, Roger      120
Cryer, C.      278
Cubic spline      230 234
Davis and Rabinowitz      64 143
Davis, P.J.      iii vii 50 51 59 66 67 137 261 266 270
de Boor and Pinkus      277
de Casteljau algorithm      271
Deutsch, Frank      59
Diagonal dominance      233
Differences ,forward      169
Differences and derivatives      34
Differences, backward      36
Differences, central      40
Differences, divided      5
Differences, q-differences      43
Divided differences      5
Divided differences and derivatives      10
Divided differences, Leibniz rule      34
Divided differences, recurrence relation      6
Divided differences, symmetric form      5
Edwards, C.H.      31
Ehlich and Zeller      108
Equioscillation      87
Erdoes, Paul      106
Euclidean space      163
Euler constant      108
Euler — Maclaurin formula      137 160
Euler, Leonhard      133 295 299
Extrapolation to the limit      140
Extreme points      69
Factorization      see “Matrix factorization”
Fejer, L.      87 248
Ferrers graph      300
Ferrers, N.M.      300
Forward difference formula      30
Forward differences      28
Forward differences and derivatives      34
Forward substitution      5 21
Fourier series      57 137
Functional, linear      149
Fundamental polynomial      3 182
Gamma function      66
Gauss integration      143 153
Gauss interpolation      41
Gauss polynomials      292
Gauss — Chebyshev rule      146
Gauss — Legendre rule      143
Gauss, C.F.      41
Gaussian polynomial      292
Generating function      17 299
Gohberg and Koltracht      24
Goldstine, H.H.      31
Goodman, Oruc and Phillips      280
Goodman, T.N.T.      v 276 279
Gregory integration      139
Gregory interpolation      31
Gregory, James      vi 31
Hardy and Wright      295 299
Harriot, Thomas      31
Hermite interpolation      14
Hermite — Fejer operator      266
Hermite, C.      14
Higham, N.J.      25
Homogeneous coordinates      198
Hoschek and Lasser      271
Howie, John M.      8
Hyperbolic paraboloid      167
Inner product      59
Integration rules product rule      172
Integration rules with end correction      126 162
Integration rules, composite      125
Integration rules, Gauss — Chebyshev      146
Integration rules, Gauss — Legendre      143
Integration rules, Gaussian      143 153
Integration rules, Gregory's      139
Integration rules, interpolatory      119
Integration rules, midpoint      120 132 143 152 162
Integration rules, Newton — Cotes      120
Integration rules, rectangular      131
Integration rules, Romberg's      139
Integration rules, Simpson's      121 129 161
Integration rules, three-eighths      123 154 155
Integration rules, trapezoidal      121 125 126
Interpolating polynomial      3
Interpolating polynomial Gaussian formulas      41
Interpolating polynomial in one variable      28
Interpolating polynomial on a triangle      195
Interpolating polynomial, accuracy of      8 10 103
Interpolating polynomial, backward difference form      37
Interpolating polynomial, central difference form      41
Interpolating polynomial, divided difference form      5
Interpolating polynomial, forward difference form      30
Interpolating polynomial, Lagrange form      3
Interpolating polynomial, linear      1 2
Interpolating polynomial, multivariate      163
Interpolating polynomial, q-difference form      46
Interpolating polynomial, Stirling's form      42
Jackson, Dunham      117
Jacobi polynomials      65
Jacobian      190
Karlin, S.      275
Kocak and Phillips      47 241
Kocak, Z.F.      v
Kronecker delta      14
Lagrange interpolation      3
Lagrange, J.L.      3
Least squares approximation      82
Lebesgue constant      100
Lebesgue function      101
Lebesgue, Henri      101
Lee and Phillips      198 214
Lee, S.L.      v
Legendre coefficient      57
Legendre polynomial      52 65 143
Legendre series      57
Legendre, A.M.      52
Leibniz rule for derivatives      34
Leibniz rule for divided differences      34
Leibniz rule for forward differences      34
Leibniz rule for q-differences      47
Leibniz, Gottfried      34
Lindemann, C.L.F.      vi
Linear functional      149
Linear interpolation      1
Linear interpolation, accuracy of      9 152
Linear operator      248
Luttmann and Rivlin      108
Maclaurin, Colin      vi 133
Marsden identity      222
Marsden, M.J.      222
Matrix factorization      19 20
Matrix, banded      276
Matrix, lower triangular      18
Matrix, totally positive      274
Matrix, tridiagonal      233
Matrix, upper triangular      18
Maxwell, E.A.      200
Maxwell, James Clerk      174
Mean value theorem      124
Midpoint rule      120 132 143 152 162
Minimax approximation      87
Minkowski's inequality      50
Minor, principal      18
Modulus of continuity      116 261
Monotone operator      249 263
Monotone operator theorem      263
Multivariate interpolation      163
Natural spline      235
Neville — Aitken algorithm      11 12 186 197
Neville, E.H.      11
Newton integration rules      120
Newton Interpolation      4
Newton matrix      4 15 26
Newton — Cotes rules      120
Newton, Isaac      31
Norm      49
Open Newton — Cotes      120 132
Operator, Bernstein      248
Operator, monotone      249 263
Operator, positive      249
Orthogonal basis      52
Orthogonal polynomials      64
Orthogonal polynomials, Chebyshev      67
Orthogonal polynomials, Jacobi      65
Orthogonal polynomials, Legendre      52
Orthogonal polynomials, second kind      75
Orthogonal polynomials, ultraspherical      65
Orthonormal basis      52
Oruc and Phillips      24 270
Orug, H.      v 24
Pappus's Theorem      199
Partitions      299
Pascal identities      292
Peano kernel      149 156
Peano, Giuseppe      149
Pencil of lines      195
Pencil of planes      210
Phillips and Taylor      233 234
Phillips, G.M.      31 271
Polynomial      see “Interpolating polynomial” “Orthogonal
Positive operator      249
Powell, M.J.D.      108
Product rule      172
q-differences      43
q-integer      291
Quadratic spline      224 231
Reciprocal polynomial      297
Rectangular rule      131
Remez algorithms      93
Remez, E.Ya.      93
Richardson, L.F.      140
Rivlin, T.J.      vii 55 70 101 107 108 261
Rodrigues formula      55
Rolle's theorem      8
Romberg integration      139
Romberg, Werner      139
Schoenberg, I.J.      v 216
Sendov and Popov      117
Simpson's rule      121 159 161
Simpson's rule composite form      129
Simpson's rule error term      129
SPLINE      135 148 215
Spline interpolating      235
Spline with q-integer knots      239
Spline, B-spline      218
Spline, natural      235
Stancu, D.D.      187
Stirling factorial formula      63
Stirling interpolation      42
STIRLING, JAMES      42
Stroud, A.H.      194
Submatrix, principal      18
Support, interval of      218
Symmetric function, complete      16 32
Symmetric function, elementary      16
Taylor polynomial      11 147
Taylor, Brook      vi
Taylor, P.J.      vi
Tetrahedron of reference      209
Three-eighths rule      123 154 155
Total positivity      274
Trapezoidal rule      121 151
Trapezoidal rule composite form      125
Trapezoidal rule error term      125 126
Trapezoidal rule with end correction      126 158
Triangle inequality      49
Triangle of reference      198
Tridiagonal matrix      233
Truncated power function      148
Turnbull, H.W.      vi
Ultraspherical polynomials      65
Uniform B-spline      229
Unimodal function      225
Unimodal polynomial      297
Unit point      199 209
Univariate interpolation      163
Vallee Poussin, C.J. de la      96
Vandermonde matrix      2 15 26 275
Vandermonde matrix, factorization of      22
Variation-diminishing      276 281
Voronovskaya theorem      261
Voronovskaya, E.V.      260
Weierstrass theorem      87 247
Weierstrass, Karl      87
Weight function      64
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