A distributed block approach to solving near-block-diagonal systems with an application to a large macroeconometric model

This paper demonstrates two advantages of well-known block variants of standard algorithms for solving nonlinear systems. First, if a problem is suf­ficiently close to block-diagonal, block algorithms may offer significant speed advantages on a single processor. Second, block Jacobi algorithms can easily and efficiently be distributed across multiple processors. We illustrate the use of a distributed block Jacobi algorithm to solve a large nonlinear macroe­conometric model. For our application, on a four-processor Unix server, the algorithm achieves a speedup factor of more than 6 over the standard algo­rithm on a single processor. A speedup factor of about 2 is due to the added efficiency of the block algorithm on a single processor, and the remaining factor of 3 results from distributing the work over four processors.