Prof. Haizhao Yang, Purdue University
Title: $O(N \log^\alpha N)$ matvec and preconditioners for highly oscillatory integral transforms
Abstract: One of the key problems in scientific computing is the acceleration of matrix computation for large problem sizes. This talk introduces several $O(N \log^\alpha N)$ algorithms for dense matrix multiplications and solving linear systems from highly oscillatory phenomena, e.g, evaluating oscillatory integral transform and special function transforms, performing their inverse transforms, solving boundary integral equations in the high-frequency regime, etc. Based on recent advances of randomized numerical linear algebra and matrix recovery, we are able to approximate these dense matrices and their inverse in $O(N \log^\alpha N)$ operations, leading to efficient matvec and preconditioners for highly oscillatory integral transforms.