SS6 - Symbolic Linear Algebra and Its Applications
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Symbolic Linear Algebra is now a mature subject at the heart of symbolic computation, with many important sub-disciplines and complementary aspects. Fundamentally, the field is concerned with computing with linear operators and matrices of mathematical entries, whether over an exact domain (such as the integers or a finite field), structured types (such as univariate or multivariate polynomials, with exact or approximate coefficients), or even more general fields and rings (such as differential operators). Enormous strides have been made in the development of algorithms and their realization in innovative software libraries and computer algebra systems. But even after six decades or more of theory and practice, progress is still being made in the efficiency and complexity, scope of matrix operations, diversity of underlying domains, and exploitation of matrix structure. Moreover, all advances have the potential to increase the ability for computer algebra systems to solve larger and more interesting problems and increase their field of application.
In this broad session, we will consider all aspects of the above, including:
- Algorithms for multivariate and parameterized matrices
- Structured linear algebra, e.g. for totally nonnegative matrices
- Sparse matrices and sparse domains
- Black-box and iterative matrix methods
- Complexity of linear algebra algorithms and problems
- Symbolic-numeric methods and stability analyses
- Matrices of differential and difference (Ore) polynomials
- Bohemian matrices, random matrices and experimental matrix algebra
- Implementation and libraries for symbolic linear algebra
We will be especially interested in the application of established and novel symbolic linear algebra techniques, software, and systems to real-world problems.
Session organizers
| Robert M. Corless (University of Western Ontario, London, Ontario, Canada) |
| Mark Giesbrecht (Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada) |