H-Matrix and Block Error Tolerances

2011/10/12 by Andrew Bradley, Bradley, Andrew M.
Computer Science · Engineering · Physics and Astronomy · #15A60 #65D15 #65F35 #65M38 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1110.2807

openalex publication_date 2011/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a new method to map the requested error tolerance on an H-matrix approximation to the block error tolerances. Numerical experiments show that the method produces more efficient approximations than the standard method for kernels having singularity order greater than one, often by factors of 1.5 to 5 and at a lower computational cost.

Related

• Adaptive multiplication of H²-matrices with block-relative error control
• Floating Point Compression of Hierarchical Matrix Formats and its Impact on Matrix-Vector Multiplication
• Entrywise error bounds for low-rank approximations of kernel matrices
• Block-adaptive Cross Approximation of Discrete Integral Operators
• Kernel-independent adaptive construction of H²-matrix approximations