Hybrid symbolic-numeric algorithms for computational convex analysis

Hybrid Symbolic-Numeric Methodology: Views and Visions

We used computer aided symbolic computation in our previous papers to explore solutions of partial differential equations in a way that involves a synergistic application of symbolic and numeric methodologies. Here we review the results thus far and present a few examples of this emerging methodology applied to the nonlinear Burgers equation. The continued development of the hybrid methodology ...

A Fast Hybrid Symbolic-Numeric Solver for Secular Equations

In this paper we develop a hybrid symbolic-numeric fast method for solving the secular equation associated with a diagonal plus rank-one eigenvalue problem of order n in O(n) operations and O(n) storage. AMS classification: 65F15

Hybrid Symbolic and Numeric Operators as Tools for Analysis of Freeform Surfaces

Freeform surfaces are commonly used in Computer Aided Geometric Design so accurate analysis of surface properties is becoming increasingly important In this paper we de ne surface slope and surface speed develop visualization tools and demonstrate that they can be useful in the design process Generally surface properties such as curvature and twist are evaluated at a nite set of predetermined s...

Symbolic-Numeric Algebra for Polynomials

Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models

A computational scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms implemented in Maple is shown by examples of spheroidal quantum dot models, for which energy spectra and eigenfunctions versus the spheroid aspect ratio wer...