Quasiseparable LU decay bounds for inverses of banded matrices

2025/06/19 by Boito, Paola, Eidelman, Yuli
#15A09 #15B99 #65F99 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2506.16339

Abstract

We develop new, easily computable exponential decay bounds for inverses of banded matrices, based on the quasiseparable representation of Green matrices. The bounds rely on a diagonal dominance hypothesis and do not require explicit spectral information. Numerical experiments and comparisons show that these new bounds can be advantageous especially for nonsymmetric or symmetric indefinite matrices.

Citations

• Computation of quasiseparable representations of Green matrices
• Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices
• Block diagonal dominance of matrices revisited: bounds for the norms of inverses and eigenvalue inclusion sets
• Decay bounds for the numerical quasiseparable preservation in matrix\n functions
• Inexact Arnoldi residual estimates and decay properties for functions of\n non-Hermitian matrices
• Decay properties for functions of matrices over C^*-algebras
• The university of Florida sparse matrix collection

Related

• On the decay of the inverse of matrices that are sum of Kronecker products
• Decay bounds for functions of matrices with banded or Kronecker structure
• Computation of quasiseparable representations of Green matrices
• Approximating the inverse of banded matrices by banded matrices with applications to probability and statistics
• Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices