On Generating Orthogonal Polynomials 论文

详细信息

发表期刊/会议

SIAM Journal on Scientific and Statistical Computing

发表日期

1982-09-01

发表年份

1982

摘要

We consider the problem of numerically generating the recursion coefficients of orthogonal polynomials, given an arbitrary weight distribution of either discrete, continuous, or mixed type. We discuss two classical methods, respectively due to Stieltjes and Chebyshev, and modern implementations of them, placing particular emphasis on their numerical stability properties. The latter are being studied by analyzing the numerical condition of appropriate finite-dimensional maps. A number of examples are given to illustrate the strengths and weaknesses of the various methods and to test the theory developed for them.