Excerpt from Solving Sparse Triangular Linear Systems Using Fortran With Parallel Extensions of the Nyu Ultracomputer Prototype
First use equation 1 to solve for the first solution component.
Given this first component, solve either equation 2 for the second component or equation 6 for the sixth component, since these couple only to component 1. Equations 2 and 6 can be solved in parallel.
Having computed components 1, 2, and 6, then, equations 3, 4, and 7 can be solved simultaneously to give components 3, 4, and 7.
Finally, with these components known, equations 5 and 8 can be solved in parallel for components 5 and 8.
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