Abstract: In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.
Abstract: Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.
Abstract: In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.
Abstract: In this paper we introduce an efficient solution
method for the Eigen-decomposition of bisymmetric and per
symmetric matrices of symmetric structures. Here we decompose
adjacency and Laplacian matrices of symmetric structures to submatrices
with low dimension for fast and easy calculation of
eigenvalues and eigenvectors. Examples are included to show the
efficiency of the method.
Abstract: A new conceptual architecture for low-level neural
pattern recognition is presented. The key ideas are that the brain
implements support vector machines and that support vectors are
represented as memory patterns in competitive queuing memories. A
binary classifier is built from two competitive queuing memories
holding positive and negative valence training examples respectively.
The support vector machine classification function is calculated in
synchronized evaluation cycles. The kernel is computed by bisymmetric
feed-forward networks feed by sensory input and by
competitive queuing memories traversing the complete sequence of
support vectors. Temporary summation generates the output
classification. It is speculated that perception apparatus in the brain
reuses structures that have evolved for enabling fluent execution of
prepared action sequences so that pattern recognition is built on
internalized motor programmes.