Hybrid Symbolic-Numeric Computing in Distributed LSC Environments

University Of North Georgia, Dahlonega GA

Investigators

Abstract

Proposal #0098175 Hitz, Markus A. North Georgia College Data collected in experiments, or constants in physics and other sciences are of limited precision, introducing some degree of uncertainty in computations. Traditional exact methods fail to reveal the entire set of solutions to algebraic problems that have uncertain parameters. Often, these problems are inherently ill-conditioned, such that numerical methods become sensitive to small perturbations of the input parameters. Hybrid symbolic-numeric algorithms have proven to be successful for finding "nearest" solutions of problems that cannot be solved exactly. Efficient (polynomial time) algorithms have been developed for common problems, such as computing approximate GCDs of univariate polynomials. For other problems, e.g., finding the nearest singular Hankel or Toeplitz matrix, it is currently unknown whether there exist efficient algorithms. This project will continue research in this area, in particular on the problem of approximate bivariate and multivariate factorization. For both areas, symbolic and numeric computing, vast software libraries and programming environments are readily available. For hybrid computing those libraries either have features that are computationally expensive (symbolic), or lack symbolic support at all (numeric). A new class of systems adds Limited Symbolic Capabilities (LSC) to existing libraries that have optimized implementations of rational and floating point arithmetic. We will investigate, and contribute to, LSC systems. This is an RUI project. Undergraduate students will engage in research that is appropriate for their level of expertise. In the process they will also gain valuable skills in configuring local area networks, and in operating clusters of computers which become more and more important in server applications.