We continue to formalize the concept of the Generalized Full Addition and Subtraction circuits (GFAs), define the structures of calculation units for the Redundant Signed Digit (RSD) operations, then prove its stability of the calculations. Generally, one-bit binary full adder assumes positive weights to all of its three binary inputs and two outputs. We define the circuit structure of two-type...

Abstract Profile monitoring in statistical quality control has attracted attention of many researchers recently. A profile is a function between response variables and one or more independent variables. There have been only a limited number of researches on monitoring multivariate profiles. Indeed, monitoring correlated multivariate profiles is a new subject in the fileld of statistical proces...

The need to evaluate expressions of the form f(A) or f(A)b, where f is a nonlinear function, A is a large sparse n × n matrix, and b is an n-vector, arises in many applications. This paper describes how the Faber transform applied to the field of values of A can be used to determine improved error bounds for popular polynomial approximation methods based on the Arnoldi process. Applications of ...

An attempt is made to clarify the position as to the comparative two-dimensional velocity distributions on a thin doubly symmetrical aerofoil and on the corresponding senli-infmite body, the front part being the same ill the two cases. It is shown that the approximate linear method may be used with advantage to investigate the problem. The method provides a simple general proof that the superve...

A simple algorithm for lattice reduction of polynomial matrices is described and analysed. The algorithm is adapted and applied to various tasks, including rank profile and determinant computation, transformation to Hermite and Popov canonical form, polynomial linear system solving and short vector computation. © 2003 Elsevier Science Ltd. All rights reserved.

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, s...