Hybrid Symbolic-Numeric Computation

26th International Conference on Applications of Computer Algebra (ACA)
July 23-27, 2021, Virtual, Online

Organizers

Robert M. Corless, Mark Giesbrecht, George Labahn, Leili Rafiee Sevyeri,

David R. Cheriton School of Computer Science, University of Waterloo, Canada

Traditionally there have been relatively separate threads of research in computational mathematics: numerical/approximate and symbolic/exact. In the past two decades, due to the demands of efficiency, reliability and accuracy in scientific and engineering computations, aspects of these two approaches have come together into what is now known as hybrid symbolic-numeric computation. Advances in algorithms, implementation, and mathematics have supported this direction.

Polynomials, together with matrices, are the natural tools used in algebraic and numeric computations. In many real-life problems the polynomial data is accessible only with noise (small perturbations in coefficients or entries) and approximation due to computing resources. Computing with these approximate polynomials and matrices form a major part of hybrid symbolic-numeric computation.

The aim of this session is to gather experts in symbolic-numeric computation to discuss and share the most recent achievements and open problems. The main focus of this meeting is on approximate polynomial and matrix algebras, and related applications.

Topics of interest include:

GCD and factorization for polynomials with inexact coefficients

Symbolic-numeric methods for solving polynomial systems

Design and implementation of symbolic-numeric algorithms

Applications of symbolic-numeric computation

Sparse interpolation and exponential analysis and sparse signal processing

Alternative bases

Matrix polynomials (e.g low-rank approximations, normal forms,...)

Backward-error and optimization-based algorithms and analysis

Talks:

• Approximation of functions of structured matrices, Paola Boito, Università di Pisa

• Symbolic-numeric computing for Bohemian matrices , Rob Corless, University of Waterloo

• Sparse Interpolation: from de Prony to Froissart and beyond, Annie Cuyt, University of Antwerp

• Hermite Interpolation With Error Correction , Erich Kaltofen, North Carolina State University

• Sparse Interpolation: design sparse antenna arrays for estimating directions of arriving signals, Wen-shin Lee, University of Stirling

• On the problem of the approximate parametrization of algebraic curves and surfaces and some applications , Sonia Pérez-Díaz, Universidad de Alcalá

• Linearizations of transfer function matrices, María C. Quintana, Aalto University

• Hybrid Symbolic-Numeric Computing in Linear and Polynomial Algebra , Leili Rafiee Sevyeri, University of Waterloo

• Multivariate Approximate GCD Computation Using Null Space of Subresultant Matrix within Polynomials: Non-singular Case , Masaru Sanuki, University of Tsukuba

• The Nearest Function Represented by a Convex Combination of Given Functions with Constraints, Hiroshi Sekigawa, Tokyo University of Science

• Solving Irregular Triangular Systems: a Truly Local Approach, Chee Yap, New York University

• Verifying the Positivity of a Function over a Finite Set , Lihong Zhi, Academia Sinica