Hessian estimates for convex solutions to quadratic Hessian equation
- Award ID(s):
- 1800495
- PAR ID:
- 10090162
- Date Published:
- Journal Name:
- Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Volume:
- 36
- Issue:
- 2
- ISSN:
- 0294-1449
- Page Range / eLocation ID:
- 451 to 454
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We propose a novel randomized linear least squares solver which is an improvement of Iterative Hessian Sketch and randomized preconditioning. In the proposed Momentum-IHS technique (M-IHS), Heavy Ball Method is used to accelerate the convergence of iterations. It is shown that for any full rank data matrix, rate of convergence depends on the ratio between the feature size and the sketch size. Unlike the Conjugate Gradient technique, the rate of convergence is unaffected by either the condition number or the eigenvalue spectrum of the data matrix. As demonstrated over many examples, the proposed M-IHS provides compatible performance with the state of the art randomized preconditioning methods such as LSRN or Blendenpik and yet, it provides a completely different perspective in the area of iterative solvers which can pave the way for future developments.more » « less
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