Invited by Prof. Yumei Huang of School of Mathematics and Statistics, Prof. Yanfei Jing from School of Mathematical Sciences，UESTC will give a lecture.

Title: Block Krylov Solvers for Sequences of Linear Systems

Time: 10:00 a.m.,Jul. 23rd, 2021

Location: Room 518, Polytechnic building

Abstract: In this talk, we are interested in the solution of a sequence of linear systems with several right-hand sides given simultaneously or in sequence. Such problems are required in many large scientific and industrial applications, such as in Lattice QCD, radar cross section calculation in computational electromagnetism, wave scattering and wave propagation in acoustics, various source locations in seismic and so on.Block Krylov subspace methods appear as good candidates for the solution of such linear systems in the computational sciences. However, different from the “happy breakdown” in regular single Krylov solvers for solving a system of linear equations with only one right-hand side, one difficulty for applying block Krylov solvers for solving such systems rests on a common issue of rank deficiency, which might appear when expanding the residual spaces, and is caused by the convergence of individual or linear combination of solution vectors. Such rank deficiency problem could lead the block Arnoldi process to breakdown before the solutions for all the right-hand sides are found. We report two recently-developed block minimun residual norm subspace methods with addressing such rank deficiency problems. This work is joint with Emmanuel Agullo, Luc Giraud, Ting-Zhu Huang, Yan-Fei Xiang.