Techniques of reliable computing, like interval arithmetic, can be used to guarantee reliable solutions even in the presence of numerical round-off errors. The need to trace bounds for the error function separately can be eliminated using these techniques. In this extended abstract, we focus on presenting how the techniques and algorithms of reliable computing can be applied to the construction...

The hypotenuse function, z = √ x2 + y2, is sometimes included in math library packages. Assuming that it is being computed by a straightforward algorithm, in a binary floating point environment, with round to nearest rounding mode, a sharp roundoff error bound is derived, for arbitrary precision. For IEEE single precision, or higher, the bound implies that |z − z| < 1.222 ulp(z) and |z − z| < 1...

We focus on detecting insider access violations to off-topic documents. Previously, we utilized information retrieval techniques, e.g., clustering and relevance feedback, to warn of potential misuse. For the relevance feedback approach, we minimize the indicative features needed for detection using data mining techniques. We show that the derived reduced feature subset achieves equivalent perfo...

A rounding error analysis is presented for a divide-and-conquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a stable solution. The algorithm is shown to be stable for block diagonally dominant matrices and for M-matrices.

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 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...

Though new technological trends and paradigms arise for developing complex software systems, systematic reuse continues to be an elusive goal. In this context, the adoption of Commercial Off-The-Shelf (COTS) technologies introduces many challenges that still have not been fully overcome, such as the lack of comprehensive mechanisms to record and manage the required information for supporting CO...

We describe a series of algorithms which automatically control camera position in a virtual environment while a user is engaged in a simulated face-to-face dialog with a single virtual agent. The common objective of the algorithms is to increase user engagement with the interaction. In our work, we describe three different automated camera control systems that: (1) control the camera’s position...

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...