English

Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices

Rings and Algebras 2024-03-01 v2

Abstract

A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent factorizations are established, leading to semi-closed-form formulas for the inverse sum of two single-pair matrices. An application to derive the symbolic inverse of a particular Gram matrix is presented, and the numerical stability of the formulas is studied.

Keywords

Cite

@article{arxiv.2304.06100,
  title  = {Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices},
  author = {Sebastien Bossu},
  journal= {arXiv preprint arXiv:2304.06100},
  year   = {2024}
}

Comments

Working paper, 26 pages