论文信息 - Least-squares orthogonal polynomials

Least-squares orthogonal polynomials

Abstract In this paper the new notion of least-squares orthogonal polynomials is introduced. Their existence and uniqueness is studied and some methods for their recursive computation are given. The location of their zeros in the case of a positive definite functional is studied. The paper ends with applications to Pade-type approximation and Gaussian quadrature methods.

Ana C. Matos | Claude Brezinski | C. Brezinski

[1] C. Brezinski. Padé-type approximation and general orthogonal polynomials , 1980 .

[2] A. Iserles,et al. On the theory of biorthogonal polynomials , 1988 .

[3] C. Brezinski. Biorthogonality and its Applications to Numerical Analysis , 1991 .

[4] F. R. Gantmakher. The Theory of Matrices , 1984 .

[5] A. Draux. Polynômes orthogonaux formels : applications , 1983 .

[6] Claude Brezinski,et al. Recursive interpolation, extrapolation and projection * , 1983 .

[7] Claude Brezinski,et al. Extrapolation methods - theory and practice , 1993, Studies in computational mathematics.

[8] D. Faddeev,et al. Computational methods of linear algebra , 1981 .

[9] C. Brezinski,et al. A breakdown-free Lanczos type algorithm for solving linear systems , 1992 .

[10] L. Mirsky,et al. The Theory of Matrices , 1961, The Mathematical Gazette.

[11] Arieh Iserles,et al. Bi-orthogonal polynomials , 1985 .