Bounds on the singular values of matrices with displacement structure
B Beckermann, A Townsend - SIAM Review, 2019 - SIAM
Matrices with displacement structure, such as Pick, Vandermonde, and Hankel matrices,
appear in a diverse range of applications. In this paper, we use an extremal problem …
appear in a diverse range of applications. In this paper, we use an extremal problem …
General ten-instant DTDMSR model for dynamic matrix square root finding
J Chen, J Guo, Y Zhang - Cybernetics and Systems, 2020 - Taylor & Francis
Because of its extensive appearance and application in scientific research and industrial
production, the matrix square root problem has received massive attention and study. In this …
production, the matrix square root problem has received massive attention and study. In this …
Multivariate rational approximation of functions with curves of singularities
N Boullé, A Herremans, D Huybrechs - SIAM Journal on Scientific Computing, 2024 - SIAM
Functions with singularities are notoriously difficult to approximate with conventional
approximation schemes. In computational applications, they are often resolved with low …
approximation schemes. In computational applications, they are often resolved with low …
Noise‐tolerate and adaptive coefficient zeroing neural network for solving dynamic matrix square root
The solving of dynamic matrix square root (DMSR) problems is frequently encountered in
many scientific and engineering fields. Although the original zeroing neural network is …
many scientific and engineering fields. Although the original zeroing neural network is …
Flexible rational approximation and its application for matrix functions
This paper proposes a unique optimization approach for estimating the minimax rational
approximation and its application for evaluating matrix functions. Our method enables the …
approximation and its application for evaluating matrix functions. Our method enables the …
On the data-sparsity of the solution of Riccati equations with applications to feedback control
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in
various control theory applications. This work demonstrates that when the matrix coefficients …
various control theory applications. This work demonstrates that when the matrix coefficients …
Approximating the pth root by composite rational functions
ES Gawlik, Y Nakatsukasa - Journal of Approximation Theory, 2021 - Elsevier
A landmark result from rational approximation theory states that x 1∕ p on [0, 1] can be
approximated by a type-(n, n) rational function with root-exponential accuracy. Motivated by …
approximated by a type-(n, n) rational function with root-exponential accuracy. Motivated by …
Zolotarev's fifth and sixth problems
ES Gawlik, Y Nakatsukasa - arXiv preprint arXiv:2011.10877, 2020 - arxiv.org
In an influential 1877 paper, Zolotarev asked and answered four questions about polynomial
and rational approximation. We ask and answer two questions: what are the best rational …
and rational approximation. We ask and answer two questions: what are the best rational …
Rational Minimax Iterations for Computing the Matrix pth Root
ES Gawlik - Constructive Approximation, 2021 - Springer
In a previous paper by the author, a family of iterations for computing the matrix square root
was constructed by exploiting a recursion obeyed by Zolotarev's rational minimax …
was constructed by exploiting a recursion obeyed by Zolotarev's rational minimax …
[PDF][PDF] A structure-preserving doubling algorithm for the square root of regular M-matrix.
Z Wang, J Guan, A Zubair - Electronic Research Archive, 2024 - aimspress.com
The matrix square root is widely encountered in many fields of mathematics. In this paper,
based on the properties of M-matrix and quadratic matrix equations, we study the square …
based on the properties of M-matrix and quadratic matrix equations, we study the square …