Abstract: This paper proposes an efficient method for calculating the eigenvalues of large-scale exponential correlation matrices by leveraging tridiagonal matrix theory. The approach explicitly ...

The Nature Index 2025 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...

Sarah has been an editor and contributor for GameRant since 2015. She kicked off her video game journey after meeting her first Chocobo, she never looked back. After years of playing them, she decided ...

We put forward and prove a simple theorem stating that the eigenvalues of a tridiagonal matrix change their sign (as a set), once the signs of the diagonal elements of the matrix are changed. We also ...

In the current article we propose a new efficient, reliable and breakdown-free algorithm for solving general opposite-bordered tridiagonal linear systems. An explicit formula for computing the ...

Julia is inconsistent about whether SymTridiagonal is Hermitian or merely symmetric for complex types. The comment at the top of tridiag.jl says that it represents "Hermitian tridiagonal matrices".

Currently, eig and similar throw no method eigfact when applied to these types of matrices. We should be able to provide efficient LAPACK-based solvers for these types. For Tridiagonal, we can exploit ...

A block representation of the BLU factorization for block tridiagonal matrices is presented. Some properties on the factors obtained in the course of the factorization are studied. Simpler expressions ...

In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized ...