Nakajima and Tanaka showed that the algebraic eigenvalue problem occurring in the discrete ordinate and matrix operator methods can be reduced to finding eigenvalues and eigenvectors of the product of two symmetric matrices, one of which is positive definite. Here, we show that the Cholesky decomposition of this positive definite matrix can be used to convert the eigenvalue problem into one inv...

The results of minimal model calculations indicate that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By means of molecular dynamics simulations around the native conformation, which describe the protein and the surrounding solvent at the all-atom level, an accurate and compact energetic map of the native state of t...

In this short note we highlight the fact that linear blind source separation can be formulated as a generalized eigenvalue decomposition under the assumptions of non-Gaussian, non-stationary, or non-white independent sources. The solution for the unmixing matrix is given by the generalized eigenvectors that simultaneously diagonalize the covariance matrix of the observations and an additional s...

We extend the Adomian's decomposition method to work for the general eigenvalue problems, in addition to the existing applications of the method to boundary and initial value problems with nonlinearity. We develop the Hamiltonian inverse iteration method which will provide the ground state eigenvalue and the explicit form eigenfunction within a few iterations. The method for finding the excited...

This paper discusses techniques for computing a few selected eigenvalue-eigenvector pairs of large and sparse symmetric matrices. A recently developed powerful class of techniques to solve this type of problems is based on integrating the matrix resolvent operator along a complex contour that encloses the interval containing the eigenvalues of interest. This paper considers such contour integra...

Friedman has proposed a regularization technique RDA of discriminant anal ysis in the Gaussian framework RDA makes use of two regularization parameters to design an intermediate classi cation rule between linear and quadratic discriminant analysis In this paper we propose an alternative approach to design classi cation rules which have also a median position between linear and quadratic discrim...

In this paper we propose a new algorithm for the joint eigenvalue decomposition of a set of real non-defective matrices. Our approach resorts to a Jacobi-like procedure based on polar matrix decomposition. We introduce a new criterion in this context for the optimization of the hyperbolic matrices, giving birth to an original algorithm called JDTM. This algorithm is described in detail and a co...