TY  - BOOK
AU  - DeVore,Ronald A
AU  - Lorentz,G.G
TI  - Constructive approximation
T2  - Grundlehren der mathematischen Wissenschaften
SN  - 3540506276
AV  - QA221 .D44 1993
PY  - 1993///]
CY  - Berlin, New York
PB  - Springer-Verlag
KW  - Approximation theory
N1  - Includes bibliographical references (pages [434]-446) and index; Contents; Ch. 1	Theorems of Weierstrass; 1	Basic Notions; 2	Approximation by Integral Operators; 3	The Theorem of Korovkin; 4	Theorems of Stone-Weierstrass; Ch. 2	Spaces of Functions; 1	Introduction. The Spaces C and L[subscript p]; 2	Rearrangement-Invariant Function Spaces; 3	Hardy's Inequalities and the ([theta],q)-quasi-norms; 4	Linear Operators. Interpolation of Operators; 5	Spaces of Differentiable Functions: Sobolev Spaces; 6	Moduli of Continuity; 7	Moduli of Smoothness; 8	Marchaud Inequalities; 9	Lipschitz Spaces; 10	Besov Spaces; Ch. 3	Best Approximation; 1	Introduction: Existence of Best Approximation; 2	Kolmogorov's Theorem; 3	Haar Systems; 4	Uniqueness of Best Approximation in C(A); 5	Chebyshev's Theorem; 6	Chebyshev Polynomials; 7	Strong Unicity; 8	Remez Algorithms; 9	Krein's Theorem; 10	Best Approximation in L[subscript p], [actual symbol not reproducible]; 11	Polya and Descartes Systems; 12	Weak Haar Systems; Ch. 4	Properties of Polynomials; 1	Inequalities of Bernstein, Szego and Markov; 2	Polynomials on the Complex Plane and in Banach Spaces; 3	Bernstein Inequalities in L[subscript p], 0 < p < 1; 4	Polynomials with Positive Coefficients in x, 1 - x; 5	Lagrange Interpolation; 6	Hermite Interpolation; 7	Divided Differences; 8	Quadrature Formulas; 9	Birkhoff Interpolation; 10	Regularity of Birkhoff Matrices; Ch. 5	Splines; 1	Definitions and Simple Properties; 2	B-Splines; 3	B-Spline Series; 4	Quasi-Interpolant Operators; 5	Euler and Bernoulli Splines; 6	Definition of Splines by Their Extremal Properties; 7	The Kolmogorov-Landau Inequalities; 8	Zero Count for Splines; 9	Spline Interpolation; 10	Sign Variation of Splines; 11	Total Positivity of the B-Spline Collocation Matrix; Ch. 6	K-Functionals and Interpolation Spaces; 1	K-Functionals; 2	K-Functionals and Moduli of Smoothness; 3	Comparisons of Moduli of Smoothness; 4	Two Theorems of Whitney; 5	Averaged Moduli of Smoothness; 6	Moduli of Smoothness with Weights; 7	The [theta],q-Interpolation Spaces; Ch. 7	Central Theorems of Approximation; 2	Trigonometric Approximation; 3	Inverse Theorems of Trigonometric Approximation; 4	Favard's Theorems; 5	Improvement of Estimates; 6	Approximation by Algebraic Polynomials; 7	Spline Approximation; 8	Approximation of Analytic Functions; 9	Approximation Spaces; Ch. 8	Influence of Endpoints in Polynomial Approximation; 2	Local Inequalities for Polynomials; 3	Properties of the Jackson Operators P[subscript n,m](f); 4	Simultaneous Approximation of Functions and Their Derivatives; 5	Brudnyi's Theorem; 6	Inverse Theorems; 7	Approximation Spaces for Algebraic Polynomials; Ch. 9	Approximation by Operators; 2	Computation of Some Norms; 3	Examples of Linear Polynomial Operators; 4	Positive Operators; 5	Projections onto Spaces Spanned by Exponentials; 6	Lower Bounds; 7	Projections in Arbitrary Banach Spaces; 8	Families of Commuting Operators; Ch. 10	Bernstein Polynomials; 1	Definitions and Inequalities; 2	Derivatives of Bernstein Polynomials; 3	Approximation and Shape Preserving Properties; 4	Bernstein Polynomials of Convex Functions; 5	Saturation and Inverse Theorems; 6	Saturation Theorems for Kantorovich Polynomials; 7	Characterization of Approximation Spaces; 8	Further Properties and Variants of Bernstein Polynomials Weak Haar Spaces; Ch. 11	Approximation of Classes of Functions, Muntz Theorems; 1	Approximation by Fourier Sums; 2	Saturation Classes; 3	Saturation of the Fejer Operators; 4	Theorems of Korneichuk; 5	Muntz' Theorem. Approximation of Monomials; 6	Case When [actual symbol not reproducible]. Selection of Best Powers; Ch. 12	Spline Approximation; 2	Splines with Equally Spaced Knots; 3	Approximation by Dyadic Splines; 4	Splines with Free Knots; 5	Smoothness in L[subscript p] for 0 < p < 1; 6	Dyadic Splines in L[subscript p], 0 < p < 1; 7	Comparison of the Spaces [actual symbol not reproducible]; 8	Free Knot Spline Approximation in L[subscript p], 0 < p < [actual symbol not reproducible]; Ch. 13	Spline Interpolation and Projections onto Spline Spaces; 1	Introduction. Lagrange Interpolation by Splines; 2	Selection of Interpolation Points; 3	Cubic Spline Interpolation; 4	Orthogonal Projection onto Splines; 5	Interpolation on R; 6	Cardinal Spline Interpolation; 7	Approximation from Shift Invariant Spaces; 8	Shape Preserving Interpolation; 9	Shape Preserving Quadratic Spline Interpolation; Bibliography; Index
ER  -