Computing symplectic eigenpairs of symmetric positive-definite matrices via trace minimization and Riemannian optimization
We address the problem of computing the smallest symplectic eigenvalues and the
corresponding eigenvectors of symmetric positive-definite matrices in the sense of …
corresponding eigenvectors of symmetric positive-definite matrices in the sense of …
The eigenvalue decomposition of normal matrices by the decomposition of the skew-symmetric part with applications to orthogonal matrices
We propose a fast method for computing the eigenvalue decomposition of a dense real
normal matrix $ A $. The method leverages algorithms that are known to be efficiently …
normal matrix $ A $. The method leverages algorithms that are known to be efficiently …
A Skew-Symmetric Lanczos Bidiagonalization Method for Computing Several Extremal Eigenpairs of a Large Skew-Symmetric Matrix
The spectral decomposition of a real skew-symmetric matrix is shown to be equivalent to a
specific structured singular value decomposition (SVD) of the matrix. Based on such …
specific structured singular value decomposition (SVD) of the matrix. Based on such …
A Chebyshev Locally Optimal Block Preconditioned Conjugate Gradient Method for Product and Standard Symmetric Eigenvalue Problems
The discretized Bethe–Salpeter eigenvalue (BSE) problem arises in many-body physics and
quantum chemistry. Discretization leads to an algebraic eigenvalue problem involving a …
quantum chemistry. Discretization leads to an algebraic eigenvalue problem involving a …
A Novel Divisional Bisection Method for the Symmetric Tridiagonal Eigenvalue Problem
W Chu, Y Zhao, H Yuan - Mathematics, 2022 - mdpi.com
The embarrassingly parallel nature of the Bisection Algorithm makes it easy and efficient to
program on a parallel computer, but with an expensive time cost when all symmetric …
program on a parallel computer, but with an expensive time cost when all symmetric …
A Power-like Method for Computing the Dominant Eigenpairs of Large Scale Real Skew-Symmetric Matrices
Q Zheng - arxiv preprint arxiv:2409.05048, 2024 - arxiv.org
The power method is a basic method for computing the dominant eigenpair of a matrix. In
this paper, we propose a structure-preserving power-like method for computing the …
this paper, we propose a structure-preserving power-like method for computing the …
Efficient and accurate algorithms for solving the Bethe–Salpeter eigenvalue problem for crystalline systems
Optical properties of materials related to light absorption and scattering are explained by the
excitation of electrons. The Bethe–Salpeter equation is the state-of-the-art approach to …
excitation of electrons. The Bethe–Salpeter equation is the state-of-the-art approach to …
A generalized skew-symmetric Lanczos bidiagonalization method for computing several extreme eigenpairs of a large skew-symmetric/symmetric positive definite …
A generalized skew-symmetric Lanczos bidiagonalization (GSSLBD) method is proposed to
compute several extreme eigenpairs of a large matrix pair $(A, B) $, where $ A $ is skew …
compute several extreme eigenpairs of a large matrix pair $(A, B) $, where $ A $ is skew …
Stable and efficient computation of generalized polar decompositions
We present methods for computing the generalized polar decomposition of a matrix based
on the dynamically weighted Halley iteration. This method is well established for computing …
on the dynamically weighted Halley iteration. This method is well established for computing …
Solving Millions of Eigenvectors in Large-Scale Quantum-Many-Body-Theory Computations
We present large-scale simulations of photovoltaics materials in the Vienna Ab initio
Simulation Package [1](VASP) that are only possible by pushing the boundaries of …
Simulation Package [1](VASP) that are only possible by pushing the boundaries of …