caa a22 4500 465821235 CHVBK 20180323112136.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF01931663 doi (NATIONALLICENCE)springer-10.1007/BF01931663 Block elimination with one refinement solves bordered linear systems accurately [Elektronische Daten] [W. Govaerts, J. Pryce] Linear systems with a fairly well-conditioned matrixM of the form $$\begin{array}{*{20}c} n \\ 1 \\ \end{array} \mathop {\left( {\begin{array}{*{20}c} A & b \\ c & d \\ \end{array} } \right)}\limits^{\begin{array}{*{20}c} n & 1 \\ \end{array} } $$ , for which a ‘black box' solver forA is available, can be accurately solved by the standard process of Block Elimination, followed by just one step of Iterative Refinement, no matter how singularA may be — provided the ‘black box' has a property that is possessed by LU- and QR-based solvers with very high probability. The resulting Algorithm BE + 1 is simpler and slightly faster than T.F. Chan's Deflation Method, and just as accurate. We analyse the case where the ‘black box' is a solver not forA but for a matrix close toA. This is of interest for numerical continuation methods. BIT Foundations, 1990 Govaerts W. Seminarie voor hogere analyse, Rijksuniversiteit-Gent, Krijgslaan 281, B-9000, Gent, Belgium aut Pryce J. Seminarie voor hogere analyse, Rijksuniversiteit-Gent, Krijgslaan 281, B-9000, Gent, Belgium aut BIT Numerical Mathematics Kluwer Academic Publishers 30/3(1990-09-01), 490-507 0006-3835 30:3<490 1990 30 10543 https://doi.org/10.1007/BF01931663 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01931663 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Govaerts W. Seminarie voor hogere analyse, Rijksuniversiteit-Gent, Krijgslaan 281, B-9000, Gent, Belgium aut NATIONALLICENCE 700 1- Pryce J. Seminarie voor hogere analyse, Rijksuniversiteit-Gent, Krijgslaan 281, B-9000, Gent, Belgium aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Kluwer Academic Publishers 30/3(1990-09-01), 490-507 0006-3835 30:3<490 1990 30 10543 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer