Includes bibliographical references (pages 317-332) and index.
CONTENTS NOTE
Text of Note
The approximation problem and existence of best approximations -- The uniqueness of best approximations -- Approximation operators and some approximating functions -- Polynomial interpolation -- Divided differences -- The uniform convergence of polynomial approximations -- The theory of minimax approximation -- The exchange algorithm -- The convergence of the exchange algorithm -- Rational approximation by the exchange algorithm -- Least squares approximation -- Properties of orthogonal polynomials -- Approximation of periodic functions -- The theory of best L1 approximation -- An example of L1 approximation and the discrete case -- The order of convergence of polynomial approximations -- The uniform boundedness theorem -- Interpolation by piecewise polynomials -- B-splines -- Convergence properties of spline approximations -- Knot positions and the calculation of spline approximations -- The Peano kernel theorem -- Natural and perfect splines -- Optimal interpolation.