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Computation of linear algebraic equations with solvability verification over multi-agent networks

Xianlin Zeng, Kai Cao (2017)

Kybernetika

In this paper, we consider the problem of solving a linear algebraic equation A x = b in a distributed way by a multi-agent system with a solvability verification requirement. In the problem formulation, each agent knows a few columns of A , different from the previous results with assuming that each agent knows a few rows of A and b . Then, a distributed continuous-time algorithm is proposed for solving the linear algebraic equation from a distributed constrained optimization viewpoint. The algorithm is...

Computation of some examples of Brown's spectral measure in free probability

Philippe Biane, Franz Lehner (2001)

Colloquium Mathematicae

We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include u ₙ + u ∞ where uₙ and u ∞ are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form S α + i S β where S α and S β are free semicircular elements of variance α and β.

Computing generalized inverse systems using matrix pencil methods

Andras Varga (2001)

International Journal of Applied Mathematics and Computer Science

We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil...

Computing the determinantal representations of hyperbolic forms

Mao-Ting Chien, Hiroshi Nakazato (2016)

Czechoslovak Mathematical Journal

The numerical range of an n × n matrix is determined by an n degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an n degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus g = 1 . We reformulate the Fiedler-Helton-Vinnikov formulae for the genus g = 0 , 1 , and present an elementary computation...

Computing the numerical range of Krein space operators

Natalia Bebiano, J. da Providência, A. Nata, J.P. da Providência (2015)

Open Mathematics

Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined...

Condition numbers of Hessenberg companion matrices

Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)

Czechoslovak Mathematical Journal

The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than...

Currently displaying 101 – 120 of 168