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MONDAY, OCTOBER 3, 2016: CME 500: Departmental Seminar
Speaker: Tim Moon, ICME Graduate student at Stanford University
"Accelerating eigenvector and pseudospectra computation using blocked multi-shift triangular solves."
Multi-shift triangular solves are basic linear algebra calculations with applications in eigenvector and pseudospectra computation. We propose blocked algorithms that efficiently exploit Level 3 BLAS to perform multi-shift triangular solves and safe multi-shift triangular solves. Numerical experiments indicate that computing triangular eigenvectors with a safe multi-shift triangular solve achieves speedups by a factor of 60 relative to LAPACK. This algorithm accelerates the calculation of general eigenvectors threefold. When using multi-shift triangular solves to compute pseudospectra, we report ninefold speedups relative to EigTool.
Location: Y2E2-111
Time: 4:30-5:20 p.m.
TUESDAY, OCTOBER 4, 2016: CME 300: First Year Seminar Series
Speakers: Gianluca Iaccarino, Associate Professor of Mechanical Engineering and Co-Director of ICME; and Eric Darve, Associate Professor of Mechanical Engineering at Stanford University
GIanluca Iaccarino will be presenting "Deep Thought: The Science of Prediction", in which he will talk about the increasing role of computational science in engineering practice and describe some of the challenges that we face in predicting performance and properties of complex physical systems. Examples from his research in uncertainty quantification and multiphysics flow simulations will be given.
Eric Darve will talk about fast linear solvers and challenges in solving large-scale PDE problems.
Location: Y2E2-101 Time: 12:30-1:20 p.m.
THURSDAY, OCTOBER 6, 2016: CME 242: Mathematical and Computational Finance
Speaker: SimonScheidegger
Abstract: Solving for the global solution of an economic model with substantial heterogeneity is very costly: The computation time and storage requirements increase dramatically with the amount of heterogeneity, i.e. with the dimensionality of the problem. It is therefore often far beyond the scope of current methods to include as much heterogeneity as a natural modeling choice would suggest. In this talk, I will present a highly parallelizable and flexible computational method to solve high-dimensional stochastic dynamic economic models. Solving such models often requires the use of iterative methods, like dynamic programming. By exploiting the generic iterative structure of this broad class of economic problems, we propose a parallelization scheme that favors hybrid massively parallel computer architectures. The solution method I will present includes the use of a fully adaptive sparse grid algorithm and the use of a mixed MPI-Intel TBB-CUDA/Thrust implementation to improve the interprocess communication strategy on massively parallel architectures. As a concrete applications of this framework, I will present results for an annually calibrated OLG model as well as a novel method for pricing American options under multi-factor models. The latter has competitive algorithmic complexity for long maturities and scales well to high-dimensional settings.
Bio: Simon Scheidegger is a Visiting Fellow at the Hoover Institution, Stanford, and a Senior Research Associate at the Department of Banking and Finance at the University of Zurich, Switzerland. His research is in computational economics and finance, high-dimensional dynamic stochastic programming, machine learning and high-performance computing. For more details please see: https://sites.google.com/site/simonscheidegger/
Location: 200-205
Time: 4:30-5:50p.m.
THURSDAY, OCTOBER 6, 2016: CME 510: Linear Algebra and Optimization Seminar
Speaker: Eric Hallman, Department of Mathematics at UC Berkeley
Title: Minimizing the Backward Error in Iterative Methods for Least-Squares Problems
Abstract: When running any iterative algorithm it is useful to know when to stop. Effective stopping criteria should be both cheap enough not to dominate the cost of the algorithm and reliable enough that the algorithm does not terminate early or too much later than necessary. Here we review LSQR and LSMR, two iterative methods for solving min_x ||Ax-b||_2 based on the Golub-Kahan bidiagonalization process, as well as stopping criteria for these methods based on estimates of the backward error. We extend LSQR and LSMR to a family of iterative algorithms and in particular introduce LSMB, an algorithm aimed at minimizing one of the backward error estimates. Tests on problems from the Florida Sparse Matrix Collection show that in practice LSMB performs as well as or better than both LSQR and LSMR.
Location: Y2E2-101
Time: 4:30-5:50 p.m.
OTHER ICME RELATED SEMINARS: Applied Math Seminar
Wednesday, October 5, 2016 Speaker: Yuan Lou, Ohio State University
Title: Evolution of diffusion in a mutation-selection model
Abstract: We consider an integro-PDE model for a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We show that in the limit of small mutation rate, the solution concentrates in the trait variable and forms a Dirac mass supported at the lowest diffusion rate. Hastings and Dockery et al. showed that for two competing species, the slower diffuser always prevails, if all other things are held equal. Our result suggests that their findings may well hold for a continuum of traits. This talk is based on joint work with King-Yeung Lam.
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