8 citations · 46 across the 18 of their papers we have counts for
17 papers · 1 filter
LSU factorization
Gennadi Malaschonok
The matrix LU factorization algorithm is a fundamental algorithm in linear algebra. We propose a generalization of the LU and LEU algorithms to accommodate the case of a commutativ…
Recursive matrix algorithms, distributed dynamic control, scaling, stability
Gennadi Malaschonok
The report is devoted to the concept of creating block-recursive matrix algorithms for computing on a supercomputer with distributed memory and dynamic decentralized control.
MathPartner: An Artificial Intelligence Cloud Service
Gennadi Malaschonok, Alexandr Seliverstov
In a broad sense, artificial intelligence is a service to find a solution to complex intellectual problems. In this sense, the MathPartner service provides artificial intelligence…
Supercomputer Environment for Recursive Matrix Algorithms
Gennadi Malaschonok, Alla Sidko
A new runtime environment for the execution of recursive matrix algorithms on a supercomputer with distributed memory is proposed. It is designed both for dense and sparse matrices…
MathPartner Computer Algebra
Gennadi Malaschonok
In this paper, we describe general characteristics of the MathPartner computer algebra system (CAS) and Mathpar programming language thereof. MathPartner can be used for scientific…
New features in MathPartner 2021
Gennadi Malaschonok, Alexandr Seliverstov
We introduce new features in the MathPartner service that have recently become available to users. We highlight the functions for calculating both arithmetic-geometric mean and geo…
Calculation of Integrals in MathPartner
Gennadi I. Malaschonok, Alexandr V. Seliverstov
We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorit…
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…
Computation of the Adjoint Matrix
Alkiviadis Akritas, Gennadi Malaschonok
The best method for computing the adjoint matrix of an order matrix in an arbitrary commutative ring requires operations, provided the complexi…
Generalized Bruhat decomposition in commutative domains
Gennadi Malaschonok
Deterministic recursive algorithms for the computation of generalized Bruhat decomposition of the matrix in commutative domain are presented. This method has the same complexity as…
Triangular Decomposition of Matrices in a Domain
Gennadi Malaschonok, Anton Scherbinin
Deterministic recursive algorithms for the computation of matrix triangular decompositions with permutations like LU and Bruhat decomposition are presented for the case of commutat…
Fast generalized Bruhat decomposition
Gennadi Malaschonok
The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix a…