Generalized fraction-free LU factorization for singular systems with kernel extraction

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. [Copyright &y& Elsevier]