Recurrence relations for orthogonal rational functions

被引：0
作者：
Miroslav S. Pranić
Lothar Reichel
机构：
[1] University of Banja Luka,Department of Mathematics and Informatics, Faculty of Science
[2] Kent State University,Department of Mathematical Sciences
来源：
Numerische Mathematik | 2013年 / 123卷
关键词：
65D30; 65D32; 41A55;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arbitrary prescribed real or complex conjugate poles. The number of terms in the recursion relation is shown to be related to the structure of the orthogonal rational functions.
引用
收藏
页码：629 / 642
页数：13
相关论文
共 28 条
[1]  
Ambroladze A.(1997)Padé-type approximants of Markov and meromorphic functions J. Approx. Theory 88 354-369
[2]  
Wallin H.(2009)Error estimation and evaluation of matrix functions via the Faber transform SIAM J. Numer. Anal. 47 3849-3883
[3]  
Beckermann B(1990)Duality in Padé-type approximation J. Comput. Appl. Math. 30 351-357
[4]  
Reichel L(2009)A matricial computation of rational quadrature formulas on the unit circle Numer. Algorithms 52 47-68
[5]  
Brezinski C(2003)Orthogonal rational functions and tridiagonal matrices J. Comput. Appl. Math. 153 89-97
[6]  
Bultheel A(2010)Orthogonality and recurrence for ordered Laurent polynomial sequences J. Comput. Appl. Math. 235 982-997
[7]  
Cantero M-J(1998)Extended Krylov subspace approximations of the matrix square root and related functions SIAM J. Matrix Anal. Appl. 19 755-771
[8]  
Bultheel A(2009)Solution of large scale evolutionary problems using rational Krylov subspaces with optimized shifts SIAM J. Sci. Comput. 31 3760-3780
[9]  
Gonzales-Vera P(2009)The extended Krylov subspace method and orthogonal Laurent polynomials Linear Algebra Appl. 431 441-458
[10]  
Hendriksen E(2011)Recursion relations for the extended Krylov subspace method Linear Algebra Appl. 434 1716-1732
123