In this part, we discuss some practical methods for computing eigenvalues and eigenvectors of matrices. Needless to say, we completely avoid trying to solve (or even write down) the characteristic polynomial equation. The very basic power method and its variants, which is based on linear iteration, is used to effectively approximate selected eigenvalues. To determine the complete system of eige...

The spatiotemporal dynamics of Lyapunov vectors (LVs) in spatially extended chaotic systems is studied by means of coupled-map lattices. We determine intrinsic length scales and spatiotemporal correlations of LVs corresponding to the leading unstable directions by translating the problem to the language of scale-invariant growing surfaces. We find that the so-called characteristic LVs exhibit s...

This paper proposes image processing algorithms to recognize five types of white blood cells in peripheral blood automatically. First, a method based on Gram-Schmidt orthogonalization is proposed along with a snake algorithm to segment nucleus and cytoplasm of the cells. Then, a variety of features are extracted from the segmented regions. Next, most discriminative features are selected using a...

We present a parallel algorithm for the QR decomposition with column pivoting of a sparse matrix by means of Modiied Gram-Schmidt orthogonalization. Nonzero elements of the matrix M to decompose are stored in a one-dimensional doubly linked list data structure. A strategy to reduce ll-in is discussed to get memory savings and decrease the computation times. As an application of QR decomposition...

The trigonometric network, introduced in this paper, is a multilayer feedforward neural network with sinusoidal activation functions. Unlike the N-dimensional Fourier series, the basis functions of the proposed trigonometric network have no strict harmonic relationship. An effective training algorithm for the network is developed. It is shown that the trigonometric network performs better than ...

We propose a 3-D sound reproduction system based on the boundary surface control principle (BoSC system) and evaluate its performance via demonstration and exhibition. The BoSC reproduction system, dome-shaped and constructed of wood, consists of 62 full-range loudspeakers and eight subwoofer loudspeakers. The BoSC recording system is designed from C80 fullerene consisting of 70 microphones of ...

Many problems in scientific computing involving a large sparse matrix A are solved by Krylov subspace methods. This includes methods for the solution of large linear systems of equations with A, for the computation of a few eigenvalues and associated eigenvectors of A, and for the approximation of nonlinear matrix functions of A. When the matrix A is non-Hermitian, the Arnoldi process commonly ...

In this paper, a new algorithm using 2DPCA and Gram-Schmidt Orthogonalization Procedure for recognition of face images is proposed. The algorithm consists of two parts. In the first part, a common feature matrix is obtained; and in the second part, the dimension of the common feature matrix is reduced. Resulting common feature matrix with reduced dimension is used for face recognition. Column a...

A novel significant vector (SV) regression algorithm is proposed in this paper based on an analysis of Chen's orthogonal least squares (OLS) regression algorithm. The proposed regularized SV algorithm finds the significant vectors in a successive greedy process in which, compared to the classical OLS algorithm, the orthogonalization has been removed from the algorithm. The performance of the pr...