We develop a new class of algorithms for general linear systems and a wide range of eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods.  This approach offers great flexibility in designing the basis for the approximation subspace, which can improve scalability in many computational environments. The resulting algorithms outperform the classic methods with minimal loss of accuracy. For model problems, numerical experiments show large advantages over MATLAB’s optimized routines, including a 100x speedup. 

Joint work with Joel Tropp (Caltech). 

The Hutchinson’s trace estimator approximates the trace of a large-scale matrix A by computing the average of some quadratic forms involving A and some random vectors. Hutch++ is a more efficient trace estimation algorithm that combines this with the randomized singular value decomposition, which obtains a low-rank approximation of A by multiplying the matrix with some random vectors. In this talk, we present an improved version of Hutch++ which aims at minimizing the computational cost - that is, the number of matrix-vector multiplications with A - needed to achieve a trace estimate with a target accuracy. This is joint work with David Persson and Daniel Kressner.