Preconditioning for linear systems arising in modeling and optimization

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A central problem in scientific computing is the solution of large systems of linear equations. Linear equations arise as a subproblem in practically every branch of computational science and engineering, including solid mechanics, fluid mechanics, electromagnetics, astrophysics, chemistry, solid and high energy physics, as well as in all manner of optimization and statistical problems. Problems as disparate as designing automobile or aircraft engines, scheduling work crews at a large company, or developing next-generation imaging devices all require solving linear equations. Indeed, for many of these problems, solving linear equations is the most computationally intensive step.