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Minisymposium “Numerical Linear Algebra Algorithms to Solve (Multivariate) Polynomial Systems” at the 2024 SIAM Conference on Applied Linear Algebra

The SIAM Conference on Applied Linear Algebra (LA24) is organized every three years and is one of the premier conferences on linear algebra. It serves as a gathering point for a diverse array of researchers from academia, research laboratories, and industries worldwide, facilitating the exchange of their most recent work and findings in applied and numerical linear algebra.

At SIAM LA24, our minisymposium delved into the connections between polynomials and (numerical) linear algebra and addressed the important task of computing the common roots of a system of (multivariate) polynomials via numerical linear algebra methods. Over the past decades, advancements in numerical algorithms have enabled the development of efficient and accurate tools to solve polynomial systems using floating-point algorithms. While the high-precision results obtained via symbolic tools could be impractical and misleading in the presence of polynomials that come from real-life applications, (numerical) linear algebra techniques are perfectly capable of dealing with inexact coefficients.

Through the talks of experts, this minisymposium illuminated the opportunities and challenges inherent in solving polynomial systems via (numerical) linear algebra. They also identified the latest trends in the field, offering valuable insights for researchers and practitioners.

Organizers:

Invited speakers:

  • Bart De Moor – “Back to the Roots of Multivariate Polynomial Systems”
  • Barbara Betti – “Solving Equations Using Khovanskii Bases”
  • Raf Vandebril – “Generating Recurrence Relations for Orthogonal Rational Functions via Inverse Eigenvalue Problems”
  • Matías Bender – “Solving Polynomial Systems Using Determinantal Formulas”
  • Lukas Vanpoucke – “Direct Numerical Computation of Polynomial Multiplication Maps”
  • Leonie Kayser – “Tensor Decomposition Using Numerical (Non)Linear Algebra”
  • Sibren Lagauw – “Solving Applications from Systems Theory via Efficient Numerical Linear Algebra Root-Finding Algorithms”