Solution of Real Matrix Eigenvalue Problem using Triplex Arithmetic

A Block Jacobi-like Method for Eigenvalue Decomposition of a Real Normal Matrix Using Real Arithmetic∗

In this paper we discuss how to design efficient Jacobi-like algorithms for eigenvalue decomposition of a real normal matrix. We introduce a block Jacobi-like method. This method uses only real arithmetic and orthogonal similarity transformations and achieves ultimate quadratic convergence. A theoretical analysis is conducted and some experimental results are presented.

Jacobi-like Algorithms for Eigenvalue Decomposition of a Real Normal Matrix Using Real Arithmetic

In this paper we introduce a method for designing efficient Jacobi-like algorithms for eigenvalue decomposition of a real normal matrix. The algorithms use only real arithmetic and achieve ultimate quadratic convergence. A theoretical analysis is conducted and some experimental results are presented.

Efficient Solution of Algebraic Bernoulli Equations Using H -Matrix Arithmetic

The algebraic Bernoulli equation (ABE) has several applications in control and system theory, e.g., the stabilization of linear dynamical systems and model reduction of unstable systems arising from the discretization and linearization of parabolic partial differential equations (PDEs). As standard methods for the solution of ABEs are of limited use for large-scale systems, we investigate appro...

Numerical solution of a quadratic eigenvalue problem

We consider the quadratic eigenvalue problem (QEP) (λ2M + λG + K)x = 0, where M = MT is positive definite, K = KT is negative definite, and G = −GT . The eigenvalues of the QEP occur in quadruplets (λ, λ,−λ,−λ) or in real or purely imaginary pairs (λ,−λ). We show that all eigenvalues of the QEP can be found efficiently and with the correct symmetry, by finding a proper solvent X of the matrix e...

Numerical Solution of the Inverse Eigenvalue Problem for Real Symmetric Toeplitz Matrices