Core Problem in Linear Algebraic Systems

• ID: 2338, RIV: 10031989
• ISSN: 0895-4798, ISBN: not specified
• source: SIAM Journal on Matrix Analysis and Applications
• keywords: Problem; Linear; Algebraic; Systems
• authors: Zdeněk Strakoš
• authors from KNM: Strakoš Zdeněk

Abstract

For any linear system Ax ~ b we define a set of core problems and show that the orthogonal upper bidiagonalization of [b,A] gives such a core problem. In particular we show that these core problems have desirable properties such as minimal dimensions. When a total least squares problem is solved by first finding a core problem, we show the resulting theory is consistent with earlier generalizations, but much simpler and clearer.