منابع مشابه
Multivariate Rational Approximation
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).
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Let F be a continuous real-valued function defined on the unit square [—1,11 x [-1, 1]. When developing the rational product approximation to F, a certain type of discontinuity may arise. We develop a variation of a known technique to overcome this discontinuity so that the approximation can be programmed. Rational product approximations to F have been computed using both the second algorithm o...
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We study nonlinear approximation in Lp(R) (0 < p < ∞, d > 1) from (a) n-term rational functions, and (b) piecewise polynomials generated by different anisotropic dyadic partitions of Rd. To characterize the rates of each such piecewise polynomial approximation we introduce a family of smoothness spaces (B-spaces) which can be viewed as an anisotropic variation of Besov spaces. We use the B-spac...
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The univariate error formulas for Pad6 approximants and rational interpolants, which are repeated in Section 2, are generalized to the multivariate case in Section 4. We deal with "general order" multivariate Pad~ approximants and rational interpolants, where the numerator and denominator polynomials as well as the equations expressing the approximation order, can be chosen by the user of these...
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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1986
ISSN: 0002-9947
DOI: 10.2307/2000277