We consider two different aspects of FETI-DP domain decomposition methods [8, 23]. In the first part, we describe an adaptive construction of coarse spaces from local eigenvalue problems for the solution of heterogeneous, e.g., multiscale, problems. This strategy of constructing a coarse space is implemented using a deflation approach. In the second part, we introduce new domain decomposition a...

We show that a Schur form of a real orthogonal matrix can be obtained from a full CS decomposition. Based on this fact a CS decomposition-based orthogonal eigenvalue method is developed. We also describe an algorithm for orthogonal similarity transformation of an orthogonal matrix to a condensed product form, and an algorithm for full CS decomposition. The latter uses mixed shifted and zero-shi...

Many scientific computing algorithms (in various domains, such as weather prediction, structural analysis, or electrical network analysis) strongly rely on solving fundamental matrix computation problems (such as linear system solving, eigenvalue decomposition, singular value decomposition, matrix nearness problems, joint diagonalization of matrices...). These problems are often solved using it...

We propose a new sufficient condition for separation of colored source signals with temporal structure, stating that the separation is possible, if the source signals have different higher self-correlation functions of even order. We show that the problem of blind source separation of uncorrelated colored signals can be converted to a symmetric eigenvalue problem of a special covariance matrix ...

We consider the smallest eigenvalue problem for symmetric or Hermitian matrices by properties of semidefinite matrices. The work is based on a floating-point Cholesky decomposition and takes into account all possible computational and rounding errors. A computational test is given to verify that a given symmetric or Hermitian matrix is not positive semidefinite, so it has at least one negative ...

In this paper an analogue of the Schwarz alternating method is considered to nd a minimal eigenvalue and its corresponding eigenvector of generalized symmetric eigenvalue problem. The technique suggested is based on decomposition of the original domain into overlapping subdomains and on consideration of local eigenvalue problems in subdomains. Both multiplicative and additive variants of the me...

In this paper we present a novel technique for wavelet-based corner detection using singular value decomposition (SVD). Here SVD facilitates the selection of global natural scale in discrete wavelet transform. We define natural scale as the level associated with most prominent (dominant) eigenvalue. Eigenvector corresponding to dominant eigenvalue is considered as the natural scale. The corners...

In this paper we present a novel technique for wavelet-based corner detection using singular value decomposition (SVD). Here SVD facilitates the selection of global natural scale in discrete wavelet transform. We de®ne natural scale as the level associated with most prominent (dominant) eigenvalue. Eigenvector corresponding to dominant eigenvalue is considered as the optimal scale. The corners ...

The paper is about a generalization of a classical eigenvalue-decomposition method originally developed for errors–in-variables linear system identification to handle an important class of nonlinear problems. A number of examples are presented to call the attention to the most critical part of the procedure turning the identification problem to a generalized eigenvalue-eigenvector calculation p...