The efficient solution of large systems of linear equations represented by sparse matrices appears in many tasks. LU factorization followed by backward and forward substitutions i...
We study the forward and backward substitution phases of a sparse multifrontal factorization. These phases are often neglected in papers on sparse direct factorization but, in man...
Patrick Amestoy, Iain S. Duff, Abdou Guermouche, T...
For when the Sylvester matrix equation has a unique solution, this work provides a closed form solution, which is expressed as a polynomial of known matrices. In the case of non-u...
Abstract. Inclusion/exclusion branching is a way to branch on requirements imposed on problems, in contrast to the classical branching on parts of the solution. The technique turne...
A parallel algorithm based on the multidimensional minimization of the Rayleigh quotient is proposed to evaluate the leftmost eigenpairs of the generalized symmetric positive defi...