8 citations · 36 across the 13 of their papers we have counts for
11 papers
LDU factorization
Gennadi Malaschonok
LU-factorization of matrices is one of the fundamental algorithms of linear algebra. The widespread use of supercomputers with distributed memory requires a review of traditional a…
Recursive Matrix Algorithms in Commutative Domain for Cluster with Distributed Memory
Gennadi Malaschonok, Evgeni Ilchenko
We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parall…
Algorithms for the Computing Determinants in Commutative Rings
Gennadi Malaschonok
Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times…
Algorithms for the solution of systems of linear equations in commutative ring
Gennadi Malaschonok
Solution methods for linear equation systems in a commutative ring are discussed. Four methods are compared, in the setting of several different rings: Dodgson's method [1], Bareis…
Effective Matrix Methods in Commutative Domains
Gennadi Malaschonok
Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed. Two of them are new. There are a methods for computing adjoined matric…
Solution of a System of Linear Equations in an Integral Ring
Gennadi Malaschonok
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoi…