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Diagonalization of a large matrix is the computational bottleneck in manyapplications such as electronic structure calculations. We show that a speedupof over 30% can be achieved by exploiting 32-bit floating point operations,while keeping 64-bit accuracy. Moreover, most of the computationally expensiveoperations are performed by level-3 BLAS/LAPACK routines in our implementation,thus leading to optimal performance on most platforms. Further improvement canbe made by using problem-specific preconditioners which take into accountnondiagonal elements.

Iterative diagonalization of symmetric matrices in mixed precision