An existence theorem for Chebyshev approximation by interpolating rationals

Numerical Chebyshev Approximation by Interpolating Rationals

The paper is concerned with the Chebyshev approximation of decay-type functions /(x) by interpolating rationals. The interpolating points are chosen to be the zeros of j(x). Existence, uniqueness and characterization of best approximations are first shown. An exchange algorithm is then described for computing the best approximation.

Approximation by Several Rationals

Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a1/q1, . . . , an/qn with smaller denominators. We show that in the special cases of n = 3 and n = 4 and certain admissible ranges for the denominators q1, . . . , qn, one can improve a result of T. H. Chan by using a different approach. 2000 Mathematics Subject ...

An Interpolating Theorem Prover

We present a method of deriving Craig interpolants from proofs in the quantifier-free theory of linear inequality and uninterpreted function symbols, and an interpolating theorem prover based on this method. The prover has been used for predicate refinement in the Blast software model checker, and can also be used directly for model checking infinite-state systems, using interpolation-based ima...

Existence Questions for the Problem of Chebyshev Approximation

This paper considers a problem of Chebyshev approximation by interpolating rationals. Examples are given which show that best approximations may not exist. Sufficient conditions for existence are established, some of which can easily be checked in practice. Illustrative examples are also presented.

Design Algorithms for Doppler MTI and Filters (Using Chebyshev Approximation)