2004/12/23 by L. A. García‐Cortés, Garcia-Cortes, L. A., C. Cabrillo +1
Computer Science · Environmental Science · Physics and Astronomy · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Scientific Research and Discoveries #Soil Geostatistics and Mapping
paper · pdf · doi:10.48550/arxiv.cs/0412107
openalex publication_date 2004/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously reported algorithm for hermitian matrices inversion based in only one draw. The use of two draws allows the inversion on non-hermitian matrices. Both the conditions for convergence and the rate of convergence are similar to the Gauss-Seidel algorithm. Results on two examples are presented, a real non-symmetric matrix related to quantitative genetics and a complex non-hermitian matrix relevant for physicists. Compared with other Monte Carlo algorithms it reveals a large reduction of the processing time showing eight times faster processing in the examples studied.