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Linear scaling algorithms: applicability, accuracy and scalable implementation

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Linear scaling algorithms are already delivering on their promise for large scale electronic structure calculations on parallel computers, but their accuracy, justification, and limits are not fully understood. Mathematically speaking these algorithms are fast approximations to the density matrix, while physically speaking they are implementations of the idea called nearsightedness. In this talk I argue that linear scaling algorithms should be useful for calculating a much wider range of matrices occurring in fields ranging from nuclear physics to engineering. I also present numerical evidence that linear scaling algorithms can be exponentially accurate even in metals as long as there is some disorder. Lastly I discuss the enormous difference between having a scalable algorithm and having an implementation which scales to the largest supercomputers, and propose a general purpose linear scaling library for calculating matrices on the largest supercomputers.

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