Dependable direct solutions for linear systems using a little extra precision
Riedy, E. Jason
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Solving a square linear system Ax=b often is considered a black box. It's supposed to "just work," and failures often are blamed on the original data or subtleties of floating-point. Now that we have an abundance of cheap computations, however, we can do much better. A little extra precision in just the right places produces accurate solutions cheaply or demonstrates when problems are too hard to solve without significant cost. This talk will outline the method, iterative refinement with a new twist; the benefits, small backward and forward errors; and the trade-offs and unexpected benefits.