Stieltjes continued fraction and QD algorithm: scalar, vector, and matrix cases
| Autor: | Jeannette Van Iseghem |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Band matrix Mathematical analysis Scalar (mathematics) Riemann–Stieltjes integral Single-entry matrix Stieltjes transformation QD algorithm Stieltjes series Hermite–Padé approximants Diagonal matrix Discrete Mathematics and Combinatorics Stieltjes continued fraction Geometry and Topology Nonnegative matrix Algorithm Mathematics Sparse matrix |
| Zdroj: | Linear Algebra and its Applications. 384:21-42 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2003.12.032 |
| Popis: | The definition, in previous studies, of vector Stieltjes continued fractions in connection with spectral properties of band operators with intermediate zero diagonals, left unsolved the question of a direct definition of their coefficients in terms of the original data, a vector of Stieltjes series. The subject was more undefined in the matrix case. A new version of the QD algorithm for matrix problem, allows to extend to the vector and matrix cases the result of Stieltjes, expansion of a (scalar) function in terms of a Stieltjes continued fraction. Beside this connection, it solves the inverse Miura transform and gives interesting identities between general band matrix and sparse band matrix. Finally, as a consequence, we extend to some dynamical systems a method known for Toda lattices. |
| Databáze: | OpenAIRE |
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