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