Advances in Numerical Methods and Matrix Computations

The field of numerical methods and matrix computations is witnessing significant developments, with a focus on improving the efficiency and accuracy of various algorithms. Researchers are exploring new approaches to solve complex problems, such as the Yang-Baxter-like matrix equation and the retrieval of top-k elements from factorized tensors. The use of neural networks and machine learning techniques is also becoming increasingly popular in this area, with applications in nonlinear solvers and preconditioned Newton methods. Additionally, there is a growing interest in the development of fast direct solvers and efficient numerical evaluation methods for various mathematical problems, including fractional Laplacian models and triple integrals. Noteworthy papers in this area include: A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers, which proposes a novel neural preconditioned Newton method for solving parametric nonlinear systems of equations. A Novel Block-Alternating Iterative Algorithm for Retrieving Top-k Elements from Factorized Tensors, which develops a block-alternating iterative algorithm for retrieving the k largest or smallest elements from a low-rank tensor. Fast Direct Solvers, which describes a class of methods known as fast direct solvers for solving systems of linear equations arising from the discretization of elliptic PDEs or integral equations.

Sources

Anti-commuting Solutions of the Yang-Baxter-like Matrix Equation

A New Initial Approximation Bound in the Durand Kerner Algorithm for Finding Polynomial Zeros

Fast Direct Solvers

A Novel Block-Alternating Iterative Algorithm for Retrieving Top-$k$ Elements from Factorized Tensors

A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers

Generalized Singular Value Decompositions of Dual Quaternion Matrix Triplets

A polynomially accelerated fixed-point iteration for vector problems

Recursive algorithms for computing Birkhoff interpolation polynomials

Modeling Closed-loop Analog Matrix Computing Circuits with Interconnect Resistance

Numerical analysis and efficient implementation of fast collocation methods for fractional Laplacian model on nonuniform grids

Efficient Numerical Evaluation of Triple Integral Using the Euler's Method and Richardson's Extrapolation

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