EM-Mo-D-01
Third Workshop on Hybrid Methodologies for Symbolic-Numeric Computation - Part I of VIII
For Part II, see EM-Mo-E-01
For Part III, see EM-Tu-D-01
For Part IV, see EM-Tu-E-01
For Part V, see EM-We-D-01
For Part VI, see EM-We-E-01
For Part VII, see EM-Th-BC-01
For Part VIII, see EM-Th-D-01

Date: August 10, Monday
Time: 13:30--15:30
Room: 311A

(Note: Click title to show the abstract.)

Organizer:
Giesbrecht, Mark (Univ. of Waterloo)
Kaltofen, Erich (North Carolina State Univ.)
Safey El Din, Mohab (Univ. Pierre & Marie Curie)
Zhi, Lihong [chair] ( Acad. of Mathematics & Sys. Sci.)

Abstract: Hybrid symbolic-numeric computation methods, which first
appeared some twenty years ago, have gained considerable
prominence. Algorithms have been developed that improve
numeric robustness (e.g., in quadrature or solving ODE
systems) using symbolic techniques prior to, or during, a
numerical solution. Likewise, traditionally symbolic
algorithms have seen speed improvements from adaptation of
numeric methods (e.g., lattice reduction methods). There is
also an emerging approach of characterizing, locating, and
solving ``interesting nearby problems'', wherein one seeks
an important event (for example a nontrivial factorization
or other useful singularities), that in some measure is
close to a given problem (one that might have only
imprecisely specified data). Many novel techniques have been
developed in these complementary areas, but there is a
general belief that a deeper understanding and wider
approach will foster future progress. The problems we are
interested are driven by applications in computational
physics (quadrature of singular integrals), dynamics
(symplectic integrators), robotics (global solutions of direct
and inverse problems near singular manifolds), control
theory (stability of models), and the engineering of
large-scale continuous and hybrid discrete-continuous
dynamical systems. Emphasis will be given to validated
and certified outputs via algebraic and exact techniques,
error estimation, interval techniques and optimization
strategies.

Our workshop will follow up on the seminal SIAM-MSRI
Workshop on Hybrid Methodologies for Symbolic-Numeric
Computation held in November 2010 and the Fields Institute
Workshop on Hybrid Methodologies for Symbolic-Numeric
Computation, November 16-19, 2011 at the University of
Waterloo, Canada. We will provide a forum for researchers on
all sides of hybrid symbolic-numeric computation.

EM-Mo-D-01-1
13:30--14:30
Hybrid symbolic-numeric computation: a marriage made in heaven
Kaltofen, Erich (North Carolina State Univ.)
Abstract: Hybrid algorithms use floating point arithmetic for speed and symbolic computation for the type of objects: formulas and exact identities and inequalities. New hybrid algorithms are presented: for solving optimization problems by sum-of-squares proofs; for computing a sparse interpolant in power or Chebyshev basis via linear progressions. There, we allow for errors in the inputs, performing error-correction by methods from digital error correcting codes. Joint with Andrew Arnold, Clement Pernet, Zhengfeng Yang, Lihong Zhi.

EM-Mo-D-01-2
14:30--15:00
Applying symbolic sparse interpolation techniques to numeric data
Roche, Daniel (U.S. Naval Acad.)
Abstract: We examine the problem of discovering a sparse polynomial from noisy samples at chosen points. Recent progress in efficient sparse interpolation algorithms over exact domains such as integers and finite fields is based on reducing the problem with potentially large degree to a related one with much lower degree. We will discuss the challenges and successes in adapting these techniques to the numeric setting.

EM-Mo-D-01-3
15:00--15:30
Sparse polynomial interpolation with arbitrary orthogonal polynomial bases
Yang, Zhengfeng Yang (East China Normal Univ.)
Abstract: The problem of sparse interpolation with arbitrary orthogonal bases can be regarded as a generalization of sparse interpolation with the Chebyshev basis. In Lakshman and Saunder [1996], an algorithm, based on Prony/Blahut's method is provided to interpolate polynomials that are sparse in the Chebyshev basis (of the first kind). In this talk, we will present new algorithms for interpolating a univariate black-box univariate polynomial that has a sparse representation by allowing arbitrary orthogonal bases. This is joint work with Erich L. Kaltofen.

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