Numerical Chebyshev Approximation by Interpolating Rationals
نویسندگان
چکیده
منابع مشابه
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.
متن کاملApproximation 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 ...
متن کاملApproximation of Analytic Functions by Chebyshev Functions
and Applied Analysis 3 where we refer to 1.4 for the am’s and we follow the convention ∏m−1 j m · · · 1. We can easily check that cm’s satisfy the following relation: m 2 m 1 cm 2 − ( m2 − n2 ) cm am 2.2 for any m ∈ {0, 1, 2, . . .}. Theorem 2.1. Assume that n is a positive integer and the radius of convergence of the power series ∑∞ m 0 amx m is ρ > 0. Let ρ0 min{1, ρ}. Then, every solution y ...
متن کاملChebyshev Approximation by Exponentials on Finite Subsets
This paper is concerned with Chebyshev approximation by exponentials on finite subsets. We take into account that varisolvency does not hold for exponentials in general. A bound for the derivatives of exponentials is established and convergence of the solutions for the discrete problems is proved in the topology of compact convergence on the open interval.
متن کاملThe Rate of Geodesic Cusp Excursions and Approximation by Rationals
We derive several results that describe the rate at which a generic geodesic makes excursions into and out of a cusp on a finite area hyperbolic surface and relate them to approximation with respect to the orbit of infinity for an associated Fuchsian group. This provides proofs of some well known theorems from metric diophantine approximation in the context of Fuchsian groups. It also gives new...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1972
ISSN: 0025-5718
DOI: 10.2307/2004729