数学讲坛-Fast Randomized and Matrix-Free Direct Solvers for Large Linear Systems
发布于:2018-05-15 10:37:12   |   作者:[学院] 数学学院   |   浏览次数:1070
时间:2018.5.17 16:30-17:30
地址:清水河主楼A1-513
主办:数学学院
承办:数学学院
范围:全校

报告题目:Fast Randomized and Matrix-Free Direct Solvers for Large Linear Systems

报 告 人:Prof. Jianlin Xia

报告时间:2018.5.17   16:30-17:30

报告地点:清水河主楼A1-513

 

 

报告摘要: In this talk, we discuss how randomized techniques can be used in structured matrix compression, and in turn in solving large dense and sparse linear systems. It is known that randomized sampling can help compute approximate SVDs via matrix-vector products. Such randomized ideas have been applied to some structured matrices for the fast compression of off-diagonal blocks. This leads to randomized and even matrix-free direct solvers for large dense linear systems.

   Furthermore, the techniques can be extended to sparse direct solvers, where randomization helps compress dense fill-in in the factorization into skinny matrix-vector products. This has a significant advantage over dense or structured fill-in used before, since the processing and propagation of the skinny products are much simpler. For some sparse discretized problems (often elliptic), the randomized sparse direct solvers can reach nearly O(n) complexity.

   We also show how to control the approximation accuracy in randomized structured solution, and further prove the superior backward stability of these randomized methods. Part of the work is joint with Yuanzhe Xi.

 

报告人简介:Prof. Jianlin Xia,博士毕业于美国加州大学伯克利分校,现任职于美国普渡大学数学系。主要研究兴趣包括数值线性代数、科学计算等,自2017年起担任Appl. Numer. Math.的编委,近年来在SIAM J. Sci. Comput.、SIAM J. Matrix Anal. Appl.等学术期刊上发表论文55篇。