8 citations · 46 across the 18 of their papers we have counts for
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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…
Recursive Method for the Solution of Systems of Linear Equations
Gennadi Malaschonok
New solution method for the systems of linear equations in commutative integral domains is proposed. Its complexity is the same that the complexity of the matrix multiplication.
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…