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Fraction-free matrix factors: new forms for lu and qr factors (2007).
| Content Provider | CiteSeerX |
|---|---|
| Author | Jeffrey, David J. Zhou, Wenqin |
| Abstract | Gaussian elimination and LU factoring have been greatly studied from the algorithmic point of view, but much less from the point view of the best output format. In this paper, we give new output formats for fraction free LU factoring and for QR factoring. The formats and the algorithms used to obtain them are valid for any matrix system in which the entries are taken from an integral domain, not just for integer matrix systems. After discussing the new output format of LU factoring, the complexity analysis for the fraction free algorithm and fraction free output is given. Our new output format contains smaller entries than previously suggested forms, and it avoids the gcd computations required by some other partially fraction free computations. As applications of our fraction free algorithm and format, we demonstrate how to construct a fraction free QR factorization and how to solve linear systems within a given domain. |
| File Format | |
| Publisher Date | 2007-01-01 |
| Access Restriction | Open |
| Subject Keyword | Qr Factor Fraction Free Qr Factorization Output Format New Output Format Lu Factoring Matrix System Fraction Free Output Gaussian Elimination Integer Matrix System Integral Domain Fraction-free Matrix Factor New Form Qr Factoring Fraction Free Algorithm Partially Fraction Free Computation Point View Linear System Fraction Free Lu Factoring Complexity Analysis Gcd Computation Algorithmic Point |
| Content Type | Text |