منابع مشابه
Padé and Hermite-Padé Approximation and Orthogonality
We give a short introduction to Padé approximation (rational approximation to a function with close contact at one point) and to Hermite-Padé approximation (simultaneous rational approximation to several functions with close contact at one point) and show how orthogonality plays a crucial role. We give some insight into how logarithmic potential theory helps in describing the asymptotic behavio...
متن کاملRational Approximation
Recently several authors have investigated the question of approximating certain functions by reciprocals of polynomials under the uniform norm on the positive real axis . Perhaps these results have some applications in industry and elsewhere (cf. [1, 36]) . Our present motivation is to give a detailed list of all the known results with simplified proofs in some cases and many new results and f...
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We estimate the error in approximating a function f by rational functions of degree n in the norm of Lq(Q), Q := [0,1]d. Among other things, we prove that if f is in the Sobolev space Wk(Q) and if k/d l/p + l/q > O, then f can be approximated by rational functions of degree n to an order O(n-k/d).
متن کاملDiscrete Rational Lp Approximation
In this paper, the problem of approximating a function defined on a finite subset of the real line by a family of generalized rational functions whose numerator and denominator spaces satisfy the Haar conditions on some closed interval [a, b] containing the finite set is considered. The pointwise closure of the family restricted to the finite set is explicitly determined. The representation obt...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1987
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(87)80007-9