ACM Computing Classification System (1998): G.1.2.
Moduli for numerical finding of the polynomial of the best Hausdorff approximation of the functions which differs from zero at just one point or having one jump and partially constant in programming environment MATHEMATICA are proposed. They are tested for practically important functions and the results are graphically illustrated. These moduli can be used for scientific research as well in teaching process of Approximation theory and...
In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples.
ACM Computing Classification System (1998): G.1.3.
This paper is partly supported by project NI13...
This paper is partially supported by project ISM-4 of Department for Scientific Research,
“Paisii Hilendarski” University of Plovdiv.
In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for
this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence.
2000 Mathematics Subject Classification: 65H10.
Here we give methodological survey of contemporary methods
for solving nonlinear systems of equations in Rn. The reason of this review
is that many authors in present days rediscovered such classical methods.
In particular, we consider Newton’s-type algorithms with sparse Jacobian.
Method for which the inverse matrix of the Jacobian is replaced by the
inverse matrix of the Vandermondian is proposed. A number of illustrative
numerical examples...
We introduce a modification of the familiar cut function by
replacing the linear part in its definition by a polynomial of degree p + 1
obtaining thus a sigmoid function called generalized cut function of degree
p + 1 (GCFP). We then study the uniform approximation of the (GCFP)
by smooth sigmoid functions such as the logistic and the shifted logistic
functions. The limiting case of the interval-valued Heaviside step function
is also discussed which imposes the use of Hausdorff metric. Numerical
examples...
A modification of the Nekrassov method for finding a solution
of a linear system of algebraic equations is given and a numerical example
is shown.
* This paper is partly supported by project IS–M–4 of Department for Scientific Research,
Paisii Hilendarski University of Plovdiv.
Biochemical mechanisms with mass action kinetics are usually modeled as
systems of ordinary differential equations (ODE) or bipartite graphs.
We present a software module for the numerical analysis of ODE models of
biochemical mechanisms of chemical species and elementary reactions
(BMCSER) within the programming environment of CAS Mathematica.
The module BMCSER also visualizes the bipartite graph of biochemical
mechanisms. Numerical examples, including a double phosphorylation model,
are presented...
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