Title 



Eigenvalue problems to compute almost optimal points for rational interpolation with prescribed poles


Author 


 

Abstract 



Explicit formulas exist for the (n, m) rational function with monic numerator and prescribed poles that has the smallest possible Chebyshev norm. In this paper we derive two different eigenvalue problems to obtain the zeros of this extremal function. The first one is an ordinary tridiagonal eigenvalue problem based on a representation in terms of Chebyshev polynomials. The second is a generalised tridiagonal eigenvalue problem which we derive using a connection with orthogonal rational functions. In the polynomial case (m = 0) both problems reduce to the tridiagonal eigenvalue problem associated with the Chebyshev polynomials of the first kind.  

Language 



English


Source (journal) 



Numerical algorithms.  Basel 

Publication 



Basel : 2007


ISSN 



10171398


Volume/pages 



45:1/4(2007), p. 8999


ISI 



000249858000007


Full text (Publisher's DOI) 


 

Full text (publisher's version  intranet only) 


 
