Eine Klasse von Verfahren zur Ermittlung bester nichtlinearer Tschebyscheff-Approximationen

SummaryMethods for constructing best nonlinear Chebyshev approximations are discussed. It is shown that local strong unicity is sufficient to guarantee “good numerical behaviour” of the algorithms. Applications are given for approximations by splines with free knots, rational functions, and exponential sums as well as for the approximation of functions defined by differential equations.

[1]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[2]  Characterization of best approximations by sums of exponentials , 1973 .

[3]  Bemerkungen zur Numerischen Behandlung Nichtlinearer Aufgaben der Tschebyscheff-Approximation , 1976 .

[4]  L. Collatz.  I. A. Ljusternik, W. I. Sobolew, Elemente der Funktionalanalysis. (Mathematische Lehrbücher und Monographien, Band VIII). Vierte, neubearb. u. erw. Aufl. VIII + 375 S. m. 7 Abb. Berlin 1968. Akademie‐Verlag. Preis geb. 34,– M , 1969 .

[5]  G. Alistair Watson,et al.  An Algorithm for Minimax Approximation in the Nonlinear Case , 1969, Comput. J..

[6]  An Algorithm for Discrete, Nonlinear, Best Approximation Problems , 1972 .

[7]  E. Cheney.  Introduction to approximation theory , 1966 .

[8]  J. Baxley.  Nonlinear Two Point Boundary Value Problems , 1968 .

[9]  R. Esch,et al.  Computational methods for best spline function approximation , 1969 .

[10]  D. Braess.  Die Konstruktion der Tschebyscheff-Approximierenden bei der Anpassung mit Exponentialsummen , 1970 .

[11]  H. Werner.  Vorlesung über Approximationstheorie , 1966 .

[12]  Kritische Punkte bei der nichtlinearen Tschebyscheff-Approximation , 1973 .

[13]  D. Braess.  Chebyshev Approximation by γ-Polynomials , 1973 .

[14]  Uniform rational approximation of functions of several variables , 1975 .

[15]  D. Braess.  Chebyshev approximation by spline functions with free knots , 1971 .

[16]  H. L. Loeb,et al.  On the Remez algorithm for non-linear families , 1970 .