Linear Algebra and its Applications, 436(1):27–40, January, 2012.
Linear systems are usually solved with Gaussian elimination. Especially when multiple right hand sides are involved, an efficient procedure is to provide a factorization of the left hand side. When exact computations are required in an integral domain, complete fraction-free factorization and forward–backward substitutions are useful. This article deals with the case where the left hand side may be singular. In such a case, kernels are required to test a solvability condition and to derive the general form of the solutions. The complete fraction-free algorithms are therefore extended to deal with singular systems and to provide the kernels with exact computations on the same integral domain where the initial data take their entries.
@article{dureisseix_generalized_2012,
title = {Generalized fraction-free {LU} factorization for singular systems with kernel extraction},
volume = {436},
issn = {0024-3795},
url = {http://www.sciencedirect.com/science/article/pii/S0024379511004617},
doi = {10.1016/j.laa.2011.06.013},
abstract = {Linear systems are usually solved with Gaussian elimination. Especially when multiple right hand sides are involved, an efficient procedure is to provide a factorization of the left hand side. When exact computations are required in an integral domain, complete fraction-free factorization and forward–backward substitutions are useful. This article deals with the case where the left hand side may be singular. In such a case, kernels are required to test a solvability condition and to derive the general form of the solutions. The complete fraction-free algorithms are therefore extended to deal with singular systems and to provide the kernels with exact computations on the same integral domain where the initial data take their entries.},
number = {1},
urldate = {2016-05-05},
journal = {Linear Algebra and its Applications},
author = {Dureisseix, David},
month = jan,
year = {2012},
keywords = {CFFLU, Exact factorization, Gaussian elimination, Integral domain, Linear system, mathematics, research, symbolic computation, uses sympy},
pages = {27--40},
}