In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...

A comprehensive survey of some recent results regarding parameterized inverse eigenvalue problems is given in this paper. Speciic topics include: additive and multiplicative inverse eigenvalue problems, classical inverse eigenvalue problems and generalized inverse eigenvalue problems. Both the theoretic and algorithmic aspects are reviewed. Some open problems are revealed to stimulate further r...

We summarize the basics and first results of the analyses within our ZIB Bridge Project and give an outlook on further studies broadening the usage of hardware acceleration within the Finite Element Method (FEM) based solution of Maxwell’s equations. 1 Solving the Generalized Eigenvalue Problem The main focus of our project is on the solution of the eigenvalue problem originating from Maxwell’s...

Abstract—A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some ...

In general, the optimal computational complexity of Arnoldi iteration is O(kN) for solving a generalized eigenvalue problem, with k being the number of dominant eigenvalues and N the matrix size. In this work, we reduce the computational complexity of the Arnoldi iteration from O(kN) to O(N), thus paving the way for full-wave extraction of very large-scale onchip interconnects, the k of which i...

An analytic criterion is developed to investigate generalized synchronization (GS) in unidirectionally coupled systems based on the auxiliary system approach. The criterion is derived by transforming the existence problem of generalized synchronization into an eigenvalue problem. Numerical simulations show that the analytic criterion is almost as accurate as the response Lyapunov exponents meth...

We discuss the design and development of a new Fortran code EA16 for the computation of selected eigenvalues and eigenvectors of large-scale real symmetric eigenvalue problems. EA16 can be used for either the standard or the generalized eigenvalue problem. The underlying method used by EA16 is the block Lanczos method with partial reorthogonalization plus implicit restarting, combined with purg...

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...