Methods are presented for performing a rigorous sensitivity analysis of numerical problems with independent, noncorrelated data for general systems of linear and nonlinear equations. The methods may serve for the following two purposes. First, to bound the dependency of the solution on changes in the input data. In contrast to condition numbers, a componentwise sensitivity analysis of the solut...

Methods are presented for performing a rigorous sensitivity analysis of numerical problems with independent, noncorrelated data for general systems of linear and nonlinear equations. The methods may serve for the following two purposes. First, to bound the dependency of the solution on changes in the input data. In contrast to condition numbers a componentwise sensitivity analysis of the soluti...

We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: arity can differ from that constituents, and elements different multipliers be \textquotedblleft entangled\textquotedblright\ such is no longer componentwise. The main property we want preserve associativity, gained by using associativity quiver tech...

We develop a new statistic for testing the equality of two multivariate mean vectors. A scaled chi-squared distribution is proposed as an approximating null distribution. Because the test statistic is based on componentwise statistics, it has the advantage over Hotelling's T2 test of being applicable to the case where the dimension of an observation exceeds the number of observations. An appeal...

We study the numerical behavior of stationary one-step or two-step matrix splitting iteration methods for solving large sparse systems of linear equations. We show that inexact solutions of inner linear systems associated with the matrix splittings may considerably influence the accuracy of the approximate solutions computed in finite precision arithmetic. For a general stationary matrix splitt...

The IHACRES model has been successfully applied to many catchments across the UK including regionalization studies (e.g. Sefton and Howarth, 1998; Littlewood, 2003). However, while the previous formulation of the non-linear module performs well in calibration and simulation, the module has some identified deficiencies in the representation of the impacts of climate change on volume of streamflo...

Given a linear map T on Euclidean Jordan algebra of rank n, we consider the set all nonnegative vectors q in Rn with decreasing components that satisfy pointwise weak-majorization inequality λ(|T(x)|)≺w⁡q∗λ(|x|), where λ is eigenvalue and ∗ denotes componentwise product Rn. With respect to ordering, show existence least vector this set. When positive map, shown be join (in order) T(e) T∗(e), e ...

Let I ⊂ R be a graded ideal in the polynomial ring R = K[x1, . . . , xn] where K is a field, and fix a term order <. It has been shown in [17] that the Hilbert functions of the local cohomology modules of R/I are bounded by those of R/ in(I), where in(I) denotes the initial ideal of I with respect to <. In this note we study the question when the local cohomology modules of R/I and R/ in(I) hav...