Abstract
The concept of a deflated solution to the linear system Ax equals b, where A may be nearly singular and b is not consistent with A is generalized to that of a deflated decomposition. Such decompositions are treated in a uniform framework, and some new deflated solutions based on LU-factorization are introduced. In particular, it is proved that the difference between one of the LU-based deflated solutions and the SVD-based deflated solution tends to zero as A tends to exactly singular. In addition, noniterative implicit algorithms are given for computing the LU-based decompositions. Numerical results verifying the accuracy and stability of the algorithms are presented.
Original language | English |
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Pages (from-to) | 738-754 |
Number of pages | 17 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 21 |
Issue number | 4 |
DOIs | |
State | Published - 1984 |
Externally published | Yes |
Bibliographical note
cited By 38Keywords
- Mathematical techniques