The Cholesky method for interval data
The interval Cholesky method is established to compute bounds of the solution set of a linear system \(Ax=b\), where it is assumed that \(A\) is symmetric and positive definite and where \(A\) and \(b\) vary within certain bounds. The method is defined as direct interval counter part to the well-known standard non-interval method, and hence, it is applied to the system in interval form, that is, to \(A^ Ix=b^ I\). The usual decomposition, \(A=LL^ T\) where \(L\) is a lower triangular matrix with positive diagonal entries can be gained only in a weaker form in the interval case, i.e., \(A^ I = L^ I(L^ I)^ T\). Beyond that, a second procedure is shown to deliver the same bounds as the first one. Finally, conditions are derived that guarantee the feasibility of the method, which means that division by zero does not occur.
scientific article; zbMATH DE number 540063
scientific article