Recursive structure of S-matrices and an O( m2) algorithm for recognizing strong sign solvability
An S-matrix is an m×( m+1) real matrix A such that for each matrix à of the same sign pattern as A, Ã's columns are the vertices of an m-simplex in R m that has the origin in its interior. An S ∗- matrix is one that can be made into an S-matrix by replacing some columns with their negatives. Su...
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| Published in | Linear algebra and its applications Vol. 96; pp. 233 - 247 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
1987
|
| Online Access | Get full text |
| ISSN | 0024-3795 1873-1856 |
| DOI | 10.1016/0024-3795(87)90347-8 |
Cover
| Summary: | An
S-matrix is an
m×(
m+1) real matrix
A such that for each matrix
à of the same sign pattern as
A,
Ã's columns are the vertices of an
m-simplex in
R
m
that has the origin in its interior. An
S
∗-
matrix is one that can be made into an
S-matrix by replacing some columns with their negatives. Such matrices are of interest because of their fundamental role in the study of sign solvability. New results on the recursive structure of these classes of matrices are presented here, and are used as the basis of algorithms of time complexity
O(
m
2) for recognizing members of the classes and for testing the strong sign solvability of linear systems. |
|---|---|
| ISSN: | 0024-3795 1873-1856 |
| DOI: | 10.1016/0024-3795(87)90347-8 |