The CUR matrix decomposition is an important extension of Nyström approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advantages over the existing relative-error CUR algorithms that it possesses tighter...

This paper delivers a study on the change of rank of input matrix in Extreme Learning Machine (ELM) and the relationship between the rank of input matrix and the residence error of training an ELM. From the viewpoint of data analysis, the study reveals why ELM has a decreasing residence error with the increase of number of nodes in hidden layer and what role the Sigmoid function plays in increa...

diffusion weighted imaging uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive a number of parameters that reflect the translational mobility of the water molecules in tissues. with a suitable experimental set-up, it is possible to calculate all the elements of the local diffusion tensor (dt) and derived paramet...

This paper describes a compression algorithm for probability transition matrices. The compressed matrix is itself a probability transition matrix. In general the compression is not error-free, but the error appears to be small even for high levels of compression.

Many image compression standards (JPEG, MPEG, H.261) are based on the Discrete Cosine Transform (DCT). However, these standards do not specify the actual DCT quantization matrix. We have previously provided mathematical formulae to compute a perceptually lossless quantization matrix. Here I show how to compute a matrix that is optimized for a particular image. The method treats each DCT coeffic...

A complete error calibration model with 12 independent parameters is established by analyzing the three-axis magnetometer error mechanism. The said model conforms to an ellipsoid restriction, the parameters of the ellipsoid equation are estimated, and the ellipsoid coefficient matrix is derived. However, the calibration matrix cannot be determined completely, as there are fewer ellipsoid parame...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

We consider approximations on SO(3) by Wigner D-matrix. We establish basic approximation properties of Wigner D-matrix, develop efficient numerical schemes using Wigner D-matrix for elliptic and parabolic equations on SO(3), and establish corresponding optimal error estimates. Numerical examples are presented to validate the theoretical estimates and illustrate a physical application. keywords....

Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracy--higher than the traditional condition numbers for linear systems suggest. This phenomenon is investigated by use of condition numbers appropriate to the componentwis...