Computational Complexity of Sparse Rational Interpolation
نویسندگان
چکیده
We analyse the computational complexity of sparse rational interpolation, and give the first deterministic algorithm for this problem with singly exponential bounds on the number of arithmetic operations. A preliminary version of this paper has appeared in [10] The first author would like to thank the Max Planck Institute in Bonn for its hospitality and support during the preparation of this paper. Supported in part by Leibniz Center for Research in Computer Science, by the DFG Grant KA 673/4-1, and by the SERC Grant GR-E 68297. The third author would like to thank the University of Bonn for its hospitality and support during the preparation of this paper.
منابع مشابه
Computational Complexity of Sparse Real Algebraic Function Interpolation
We estimate the complexity of a general problem for interpolating real algebraic functions given by a black box for their evaluations, extending the results of [GKS 90b, GKS 91b] on interpolation of sparse rational functions.
متن کاملSparse interpolation of multivariate rational functions
Consider the black box interpolation of a τ -sparse, n-variate rational function f , where τ is the maximum number of terms in either numerator or denominator. When numerator and denominator are at most of degree d, then the number of possible terms in f is O(dn) and explodes exponentially as the number of variables increases. The complexity of our sparse rational interpolation algorithm does n...
متن کاملRapid design andmodelling of wideband sinuous antenna reflector feeds through blended rational interpolation
This paper describes the design of sinuous antenna reflector feeds using blended rational interpolation. The blended rational interpolation method is developed to interpolate a sparse set of high-fidelity (HF) data while following the trends of a denser set of low-fidelity (LF) data. The HF data are obtained by full-wave computational electromagnetics simulations of the input impedance of a pyr...
متن کاملSparse Rational Function Interpolation with Finitely Many Values for the Coefficients
In this paper, we give new sparse interpolation algorithms for black box univariate and multivariate rational functions h = f/g whose coefficients are integers with an upper bound. The main idea is as follows: choose a proper integer β and let h(β) = a/b with gcd(a, b) = 1. Then f and g can be computed by solving the polynomial interpolation problems f(β) = ka and g(β) = ka for some integer k. ...
متن کاملProofs for Nondivisibility of Sparse Polynomials underthe Extended Riemann
Symbolic manipulation of sparse polynomials, given as lists of exponents and nonzero coeecients, appears to be much more complicated than dealing with polyno-mials in dense encoding (see e.g. GKS 90, KT 88, P 77a, P 77b]). The rst results in this direction are due to Plaisted P 77a, P 77b], who proved, in particular, the NP-completeness of divisibility of a polynomial x n ?1 by a product of spa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Comput.
دوره 23 شماره
صفحات -
تاریخ انتشار 1994