This paper deals with an application of regression analysis to the regulation of the blood-sugar under diabetes mellitus. Section 2 gives a description of Gram-Schmidt orthogonalization, while Section 3 discusses the difference between Gauss-Markov estimation and Least Squares Estimation. Section 4 is devoted to the statistical analysis of the blood-sugar during the night. The response change o...

In this paper, we propose novel blind separation techniques for multiple-input multiple-output systems based on least-squares constant modulus algorithm (LSCMA). To ensure that each output signal is extracted from different input signals, the proposed algorithms have been derived by using successive interference cancellation and Gram-Schmidt orthogonalization procedure. The performance is obser...

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...

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 ...

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is ...

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 ...

— In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equiva...