Computation of principal angles between subspaces is important in many applications, e.g., in statistics and information retrieval. In statistics, the angles are closely related to measures of dependency and covariance of random variables. When applied to column-spaces of matrices, the principal angles describe canonical correlations of a matrix pair. We highlight that all popular software code...

This document describes a gravitational N-body integration algorithm incorporating the following features: (1) it is exactly (neglecting rounding errors) time-reversible, (2) angular and linear momentum are conserved, (3) smooth switching functions are used to split potential terms into local and weak parts so that weaker long-range forces are evaluated relatively rarely and close interactions ...

We describe a new method of computing functions of highly non-normal matrices, by using the concept of approximate diagonalization. We formulate a conjecture about its efficiency, and provide both theoretical and numerical evidence in support of the conjecture. We apply the method to compute arbitrary real powers of highly non-normal matrices. 1. Introduction. Let A be a non-normal n × n matrix...

We consider the problem of inferring the probability distribution associated with a language, given data consisting of an infinite sequence of elements of the languge. We do this under two assumptions on the algorithms concerned: (i) like a real-life algorothm it has round-off errors, and (ii) it has no roundoff errors. Assuming (i) we (a) consider a probability mass function of the elements of...

This paper proposes an N stage "non-separable" two-dimensional (2D) wavelet transform (WT) for lossless / lossy unified coding of digital images. The proposed method achieves better coding performance especially at high bit rate since it has fewer rounding operations. We convert the conventional "separable" 2D WT into "non-separable" one without changing its frequency characteristics so that th...

We develop and implement a semi-numerical method for computing high order Taylor approximations of the unstable manifold at a hyperbolic fixed point of a compact infinite dimensional analytic map. Even though the method involves several layers of truncation our goal is to obtain a representation of the invariant manifold which is accurate in a large region about the fixed point. In order to ins...

This paper discusses improvements to the numerical robustness of the algorithm described in Kasper Fauerby’s “Improved Collision Detection and Response.” The algorithm addresses a common collision detection query: a moving sphere or ellipsoid vs. a set of motionless triangles. In its current form, the algorithm allows the sphere to penetrate the triangles. The sphere also displays “jittering” b...

The traditional floating point arithmetic of scientific computers is biased towards fast and easy production of numerical results without enough provision to enable the programmer to control and solve problems connected with numerical accuracy and cumulative round-off errors. The author suggests the varying length floating point arithmetic as a general purpose solution for most of these problem...

The importance of the Dempster-Shafer theory (DST) for modeling and propagating uncertainty has grown in the recent past. An obstacle for wider application of this theory in industrial practice is the lack of software support for analysts. The few tools available depend on floating point arithmetic and do not consider the inherently interval-based nature of the DST to the full extent. Therefore...

Minimizing the embedding impact is a practically feasible philosophy in designing steganographic systems. The development of steganographic systems can be formulated as the construction of distortion profile reflecting the embedding impact and the design of syndrome coding based on a certain code. The authors devise a new distortion profile exploring both the block complexity and the distortion...