A class of direct methods for linear systems
A new class of methods is proposed for solving general (determined or underdetermined, full rank or rank deficient) linear algebraic systems. The class is of direct type methods, the solution being found in a number of steps no larger than the number of equations. The class contains free parameters, say an initial matrix and two vectors to be chosen at each step. A general factorization of the coefficient matrix is implicitly performed by the algorithm and there exist parameter choices implicitly generating orthogonal, LU and Cholesky type factorizations. Computational experiments indicate that some algorithms in this class outperform in accuracy well-known classical methods on some very ill-conditioned problems.
scientific article; zbMATH DE number 3850361
scientific article