Title :
What is Hybrid Symbolic-Numeric Computation?
Author_Institution :
North Carolina State Univ., Raleigh, NC, USA
Abstract :
Hybrid symbolic-numeric computation constitutes the Fifth of my "Seven Dwarfs" of Symbolic Computation [1], which I have listed in my SNSC talk in Hagenberg in 2008. Hybridization requires that the solution of a computational mathematical problem should utilize both a numeric and a symbolic algorithmic component. The growth of the symbolic parts in scientific computing is driven by industry, as the proliferation of MapleSIM, a hybrid symbolic-numeric engineering design platform, testifies. In my talk, I will introduce two hybrid algorithms: one is our ArtinProver agorithm for proving the globality of an optimum of a rational function via an exact sum-of-squares certificate. The second is a randomized algorithm for recovering a sparse signal via a series of Hankel matrix condition number estimates. Specifically, I will discuss the important questions: what is an exact certificate, and what is the meaning of "success with high probability" in randomized algorithms with imprecise floating point data.
Keywords :
Hankel matrices; randomised algorithms; rational functions; symbol manipulation; ArtinProver agorithm; Hankel matrix condition number estimates; MapleSIM; computational mathematical problem; exact sum-of-squares certificate; globality; hybrid algorithm; hybrid symbolic-numeric computation; hybrid symbolic-numeric engineering design platform; hybridization; numeric algorithmic component; randomized algorithm; rational function; scientific computing; sparse signal; symbolic algorithmic component; symbolic computation; Algorithm design and analysis; Conferences; Industries; Interpolation; Optimization; Polynomials; Sparse matrices;
Conference_Titel :
Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2011 13th International Symposium on
Conference_Location :
Timisoara
Print_ISBN :
978-1-4673-0207-4
DOI :
10.1109/SYNASC.2011.65