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Randomized Algorithms For Preconditioner Selection With Applications To Kernel Regression, Conner Dipaolo
Randomized Algorithms For Preconditioner Selection With Applications To Kernel Regression, Conner Dipaolo
HMC Senior Theses
The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M-1A ||F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which …