A New Class of Fast Randomized Algorithms of Numerical Linear Algebra
Abstract
In many situations involving solution of systems of linear algebraic equations of the form Ax = y, what is actually required is a small number of inner products of the form (A????1y; z1), (A????1y; z2); : : :, (A????1y; zk): Evaluation of products of the form (A????1y; z) is readily reduced to the evaluation of (A????1y; y), and the latter turns out to be a much less expensive procedure than the solution of the whole system Ax = y. We propose to construct algorithms for the rapid evaluation of inner products of the form (A????1y; y), bypassing the construction of the whole solution of the linear systems. We will also apply the obtained algorithms to the solution of several problems of current interest, such as modeling electromagnetic scattering phenomena.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 10, 2018
- Source ID
- N000141812353
Entities
People
- Vladimir Rokhlin, Jr.
Organizations
- Office of Naval Research
- United States Navy
- Yale University