Controlled-term indexing (the method of choice for multimedia collections and still very popular for purely textual material), appears an expensive solution because it takes huge resources and manual indexing. It is not possible, however, to perform a well-founded asessment of various approaches to information retrieval. We discuss ways to improve controlled-term indexing and illustrate these b...

The parallel computation of the pseudospectrum is presented. The Parallel Path following Algorithm using Triangles (PPAT) is based on the Path following Algorithm using Triangles (PAT). This algorithm offers total reliability and can handle singular points along the level curve without difficulty. Furthermore, PPAT offers a guarantee of termination even in the presence of round-off errors and m...

Abstract: In earlier work we demonstrated that iterated numerical integration outperforms ”standard” multivariate integration techniques for various function classes with singularities inside the domain of integration. We focus on the accuracy requirements to be applied in different directions or combinations of directions of iterated integrals. The integrals are approximated numerically in an ...

We study the fluted fragment, a decidable fragment of first-order logic with an unbounded number of variables, originally identified by W.V. Quine. We show that the satisfiability problem for this fragment has non-elementary complexity, thus refuting an earlier published claim by W.C. Purdy that it is in NExpTime. More precisely, we consider, for all m greater than 1, the intersection of the fl...

Given N real numbers whose sum is an integer, we study the problem of finding N integers which match these real numbers as closely as possible, in the sense of Lp norm, while preserving the sum. We describe the structure of solutions for this integer optimization problem and propose an algorithm with complexity O(N logN) for solving it. In contrast to fractional rounding and randomized rounding...

In this work we develop a method for computing mathematically rigorous enclosures of some one dimensional manifolds of heteroclinic orbits for nonlinear maps. Our method exploits a rigorous curve following argument build on high order Taylor approximation of the local stable/unstable manifolds. The curve following argument is a uniform interval Newton method applied on short line segments. The ...

• DECIMAL or NUMERIC is the type of numbers represented as strings of decimal digits. This will have some upper bound on the length of representations that the system is willing to tolerate. Although internally DECIMALs are stored just like strings, they are interpreted as numbers. Therefore any leading zeros are removed. On the other hand, trailing zeros are preserved because they could indica...

A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is ne...

abstract Exponential windowing is a widely used technique for suppressing the eeects of old data as new data is added to a matrix. Speciically, given an n p matrix X n and a \forgetting factor" 2 (0; 1), one works with the matrix diag(n1 ; n2 ; : : : ; 1)X n. In this paper we examine an updating algorithm for computing the QR factorization of diag(n1 ; n2 ; : : :; 1)X n and show that it is unco...

We show that any real matrix can be rounded to an integer matrix in such a way that the rounding errors of all row sums are less than one, and the rounding errors of all column sums as well as all sums of consecutive row entries are less than two. Such roundings can be computed in linear time. This extends and improves previous results on rounding sequences and matrices in several directions. I...