For more information about this meeting, contact Yakov Pesin.

Title: | Optimal and Practical Solvers for Linear Algebraic Systems |

Seminar: | Department of Mathematics Colloquium |

Speaker: | Jinchao Xu, PSU |

Abstract: |

Given a linear system of equations Ax=b of N unknown, how do we find a solution in the most efficient way? This simple mathematical question is of fundamental importance in scientific computation. But it does not have an easy answer in generalâ€”especially when N is large. The classic Gaussian elimination method is still the most commonly used algorithm in practice, even though its computational complexity is high: it generally takes O(N^3) operations to find a solution. Can we do better with algorithms of complexity O(N^2) or even O(N)?
In this talk, I will first give an overview of the state of the art in regard to these questions in general and then present a number of (nearly) optimal algorithms for algebraic systems of equations arising from discretizing partial differential equations (such as Poisson, biharmonic, elasticity, Navier-Stokes, Maxwell, magnetohydrodynamics, and black-oil models). Mathematical optimality, practical applicability, and parallel scalability will be addressed for these algorithms and applications. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 03 / 01 / 2012 |

Time: | 04:00pm - 05:00pm |