Vector sequence transformations: Methodology and applications to linear systems

• Published in: Journal of computational and applied mathematics Vol. 98; no. 1; pp. 149 - 175
• Main Author: Brezinski, C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 05.10.1998; Elsevier
• Subjects: Convergence acceleration; Exact sciences and technology; Lanczos method; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Sciences and techniques of general use; Systems of linear equations; Vector sequence transformations; Vector sequence transformations; Systems of linear equations; Convergence acceleration; Lanczos method; Interpolation; Numerical analysis; Linear system; Linear algebra
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(98)00119-8

In this paper, a methodology for the construction of various vector sequence transformations is formulated leading to a unified presentation of the subject and to new results. The connections to the general interpolation problem and to projections are discussed. Various particular cases are examined in more details. Applications to the solution of systems of linear equations will end the paper and, in particular, their relation with Lanczos method will be studied. Some numerical examples will be given.