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This paper proposes a method for speeding up the estimation of the absolute value of largest eigenvalue of an asymmetric tridiagonal matrix based on Power method. An error analysis shows that the proposed method provide errors no greater than the usual Power method. The proposed method involves the computation of the tridiagonal matrix square under analysis, which is performed through a proposed fast...
The principal independent component analysis (PICA) network is used to the real-valued source signals blind separation with a reference. It's proved in this paper that when a reference signal is available, the blind source separation can be transformed to the eigenvalue eigenvector decomposition of a real symmetric matrix. When generalized to the multi-reference case, a similar result is obtained...
In this paper a simple infinity norm based neural network algorithm for estimation of the principal component is developed. It seems to be especially useful in applications with changing environment, where the learning process has to be repeated in online manner. Theoretical analysis shows the weight vector converges to the principal eigenvector asymptotically. In comparison with the existing algorithms,...
In this correspondence, several algorithms to compute a lower bound of the smallest eigenvalue of a symmetric positive-definite Toeplitz matrix are described and compared in terms of accuracy and computational efficiency. Exploiting the Toeplitz structure of the considered matrix, new theoretical insights are derived and an efficient implementation of some of the aforementioned algorithms is provided.
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