Matrix Inversion Using Parallel Processing
Journal of the ACM (JACM)
Some Complexity Results for Matrix Computations on Parallel Processors
Journal of the ACM (JACM)
On the performance of decentralized software
PERFORMANCE '80 Proceedings of the 1980 international symposium on Computer performance modelling, measurement and evaluation
Partitioned Matrix Algorithms for VLSI Arithmetic Systems
IEEE Transactions on Computers
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It is shown that a mesh-connected n×n multiprocessor system can compute the inverse of a n×n matrix in linear time to n. The algorithm is based on a theorem known to Sylvester in 1851. It computes the cofactor matrix in n steps, each of which involves 4 unit distance message routing and 4 arithmetic operations for every processor. A coding and memory requirement for each processor is the same and is independent of n. It is also shown that the same algorithm solves systems of n linear equations in linear time of n with n × (n+l) processors.