Many problems in applied and numerical analysis eventually boil down to solving large systems of linear algebraic equations. Since the matrices and right-hand sides of such systems are typically the result of (sometimes extensive) computations, they are subject to an unavoidable level of noise caused by the rounding errors committed during their generation. It is then a matter of practical conc...

1. INTRODUCTION When economic behavior is expressed as a continuous variable, a linear regression model is often adequate to describe the impact of economic factors on this behavior, or to predict this behavior in altered circumstances. For example, a study of food expenditures as a function of price indices for commodity groups and income, using households from the Consumer Expenditure Survey,...

This article presents rigorous normwise perturbation bounds for the Cholesky, LU and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algorithms. The used approach is a combination of the classic and refined matrix equation approaches. Each of th...

where z is a new variable. This exemplifies the procedure for an arbitrary ODE. The usual choice for the new variables is to let them be just derivatives of each other (and of the original variable). Occasionally, it is useful to incorporate into their definition some other factors in the equation, or some powers of the independent variable, for the purpose of mitigating singular behavior that ...

The problem of evaluating the sign of the determinant of a small matrix arises in many geometric algorithms. Given an n × n matrix A with integer entries, whose columns are all smaller than M in Euclidean norm, the algorithm given here evaluates the sign of the determinant detA exactly. The algorithm requires an arithmetic precision of less than 1.5n+2 lgM bits. The number of arithmetic operati...

In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is “exact” in that given the approximation inherent in the spectral-element method (SEM), no further approximation is introduced that exceeds computer round-off error. The method is very useful when the SEM has yielded an ada...

This note extends briefly the integer transforms of CM. Racier (1972) to transforms over finite fields and rings. These transforms have direct application to digital filters and make possible digital filtering without round-off error. In some cases, the parameters of such number-theoretic transforms can be chosen so that substantial reductions in hardware are possible over what would be needed ...

Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the plant equations. The present work addresses the important problem of resilience or nonfragility which is the maintenance of convergence or performance when the observer is erroneously i...

In this paper, we apply the modified variational iteration method (mVIM) for solving integrodifferential equations and coupled systems of integro-differential equations. The proposed modification is made by the elegant coupling of He’s polynomials and the correction functional of variational iteration method. The proposed mVIM is applied without any discretization, transformation or restrictive...

This paper presents a proposal of measuring uncertain modelling referred to a geometrical model obtained from a Coordinate Measuring Machine (CMM). The measurement of objects by CMM is achieved considering a particular region of measurement described through a set of nitely many points which de nes the ideal reference mesh and it is exposed to, at least, three kinds of error: systematical, alea...