Single-pass Nyström approximation in mixed precision
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Low rank matrix approximations appear in a number of scientific computing applications. We consider the Nyström method for approximating a positive semidefinite matrix A. The computational cost of its single-pass version can be decreased by running it in mixed precision, where the expensive products with A are computed in a lower than the working precision. We bound the extra finite precision error which is compared to the error of the Nyström approximation in exact arithmetic and identify when the approximation quality is not affected by the low precision computations. The mixed precision Nyström method can be used to inexpensively construct a limited memory preconditioner for the conjugate gradient method. We bound the condition number of the preconditioned coefficient matrix, and experimentally show that such preconditioner can be effective.
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