Advances in Computational Methods for Algebraic and Linear Problems

The field of computational methods for algebraic and linear problems is witnessing significant developments, with a focus on improving efficiency, accuracy, and scalability. Researchers are exploring innovative approaches to tackle complex problems, such as sparse polynomial multiplication, quaternion matrix inversion, and secure distributed matrix multiplication. These advances have the potential to impact various applications, including image processing, filtering, and deblurring. Noteworthy papers in this area include: Probably faster multiplication of sparse polynomials, which presents a probabilistic algorithm for efficient multiplication. Iterative Methods for Computing the Moore-Penrose Pseudoinverse of Quaternion Matrices, with Applications, which develops iterative methods for computing the Moore-Penrose pseudoinverse of quaternion matrices. Randomized Krylov methods for inverse problems, which proposes randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems.

Sources

Probably faster multiplication of sparse polynomials

Iterative Methods for Computing the Moore-Penrose Pseudoinverse of Quaternion Matrices, with Applications

Analog Secure Distributed Matrix Multiplication

Solving Constrained Stochastic Shortest Path Problems with Scalarisation

A Square-Root Free Algorithm for Computing Real Givens Rotations

Randomized Krylov methods for inverse problems

Refined bit complexity for the computation of at least onepoint per connected component of a smooth completeintersection real algebraic set

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