15 research outputs found
Analytical solution of a gas release problem considering permeation with time dependent boundary conditions
Numerical verification method for spectral problems (Spectral and Scattering Theory and Related Topics)
Numerical verification by infinite dimensional Newton's method for stationary solutions of the Navier-Stokes problems (New Development of Numerical Analysis in the 21st Century)
Stability of a functional equation coming from the characterization of the absolute value of additive functions
Stability of a functional equation coming from the characterization of the absolute value of additive functions
In the present paper, we prove the stability of the functional equationmax{f((x ^ y)^ y), f(x)} = f(x ^ y) + f(y)for real valued functions defined on a square-symmetric groupoid with a leftunit element. As a consequence, we obtain the known result about the stabilityof the equationmax{f(x + y), f(x ? y)} = f(x) + f(y)for real valued functions defined on an abelian grou
Validated computation tool for the Perron-Frobenius eigenvalues
A matrix with non-negative entries has a special eigenvalue, the so called Perron-Frobenius eigenvalue, which plays an important role in several fields of science [1]. In this paper we present a numerical tool to compute rigorous upper and lower bounds for the Perron-Frobenius eigenvalue of non-negative matrices. The idea is to express a non-negative matrix in terms of a directed graph, and make use of R. Tarjan’s algorithm [5] which finds all strongly connected components of a directed graph very efficiently. This enables us to decompose the original matrix into irreducible components (possibly of small size), and then to enclose the aimed Perron-Frobenius eigenvalue. We also show a numerical example which demonstrates the efficiency of our tool
Validated computation tool for the Perron-Frobenius eigenvalues
A matrix with non-negative entries has a special eigenvalue, the so called Perron-Frobenius eigenvalue, which plays an important role in several fields of science [1]. In this paper we present a numerical tool to compute rigorous upper and lower bounds for the Perron-Frobenius eigenvalue of non-negative matrices. The idea is to express a non-negative matrix in terms of a directed graph, and make use of R. Tarjan’s algorithm [5] which finds all strongly connected components of a directed graph very efficiently. This enables us to decompose the original matrix into irreducible components (possibly of small size), and then to enclose the aimed Perron-Frobenius eigenvalue. We also show a numerical example which demonstrates the efficiency of our tool