Piecewise rational approximation to continuous functions with characteristic singularities

✍ Scribed by J. Illán

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 428 KB
• Volume: 99
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(98)00157-5

✦ Synopsis

Let H/' [a,b] be the class of continuous functions in the interval [a, b], which admit analytic continuation to H p in the subintervals of a v-subdivition of [a,b]. Let S,,.,.[a,b] be the set of piecewise rational functions which have pieces of degree n and no more than v breakpoints. The paper deals with the construction of f,,,, ES,.v[a,b] close to a given f E H, P [a,b], to estimate the order of the least LP(w) distance from f to S,,,,. [a,b]. It is concluded that the piecewise rational approximation is better for Hf [a,b] than the rational one. This theory extends results of on the rational approximation to f E H~ [-1, 1], and can be applied to study the asymptotic behavior of piecewise rational methods to solve a singular identification problem associated with the equation w(2~+ (f + 2)w = 0, in terms of the error equation criterion. (~) 1998 Elsevier Science B.V. All rights reserved.