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The aim of this contribution is to propose and analyze some computational means to approximate solving mathematical problems appearing in some recent studies devoted to biological and chemical networks.

Self-correcting iterative methods for computing $2$ -inverses

Stanimirović, Predrag S. (2003)

Archivum Mathematicum

In this paper we construct a few iterative processes for computing ${2}$ -inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.

Semicoarsening multigrid for systems.

Dendy, J.E.jun. (1997)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Semi-convergence and relaxation parameters for a class of SIRT algorithms.

Elfving, Tommy, Nikazad, Touraj, Hansen, Per Christian (2010)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Several results on chordal bipartite graphs

Mihály Bakonyi, Aaron Bono (1997)

Czechoslovak Mathematical Journal

The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite graph. As consequence, occurance of arithmetic zeros will not terminate perfect Gaussian elimination on sparse matrices having associated a chordal bipartite graph. Next, a property concerning minimal edge separators is presented. Finally, it is shown that,...

Sharp lower bounds for the dimension of linearizations of matrix polynomials.

De Teran, Fernando, Dopico, Froilan M. (2008)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Simple square smoothing regularization operators.

Reichel, Lothar, Ye, Qiang (2008)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Simpler block GMRES for nonsymmetric systems with multiple right-hand sides.

Liu, Hualei, Zhong, Baojiang (2008)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Simultaneous Iteration for Computing Invariant Subspaces of Non-Hermitian Matrices.

G. W. Stewart (1975/1976)

Numerische Mathematik

Simultaneous triangularization of commuting matrices for the solution of polynomial equations

Vanesa Cortés, Juan Peña, Tomas Sauer (2012)

Open Mathematics

We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.

Smith normal form of a matrix of generalized polynomials with rational exponents

Miroslav Kureš, Ladislav Skula (2008)

Annales UMCS, Mathematica

It is proved that generalized polynomials with rational exponents over a commutative field form an elementary divisor ring; an algorithm for computing the Smith normal form is derived and implemented.

Smooth factorizations of matrix valued functions and their derivatives.

Volker Mehrmann, Peter Kunke (1991/1992)

Numerische Mathematik

Solution of a system of linear equations with given error sets for coefficients

František Šik (1982)

Aplikace matematiky

In the paper, a method is given for finding all solutions of a system of linear equations with interval coefficients and with additional supposition that these coefficients fulfil a given system of homogeneous linear equations.

Solution of Linear Equations with Hankel and Toeplitz Matrices.

J. Rissanen (1974)

Numerische Mathematik

Solution of system of linear equations with large coefficients in the diagonal

Josef Bílý (1948)

Aktuárské vědy

Solvability classes for core problems in matrix total least squares minimization

Iveta Hnětynková, Martin Plešinger, Jana Žáková (2019)

Applications of Mathematics

Linear matrix approximation problems $A X \approx B$ are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if $B$ is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of $B$ is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková,...

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