Efficient projection space updates for the approximation of iterative solutions to linear systems with successive right hand sides

Iterative solver;Projection;Solution approximation;Ax = b;Partial differential equations;Linear system;Oblique inner product;Oblique QR factorization;Updating QR factorization;Successive right hand side;Initial guess;Reduced communication

Christensen, Nicholas ; Fischer ; Paul F.

关键词: Iterative solver;    Projection;    Solution approximation;    Ax = b;    Partial differential equations;    Linear system;    Oblique inner product;    Oblique QR factorization;    Updating QR factorization;    Successive right hand side;    Initial guess;    Reduced communication;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/99410/CHRISTENSEN-THESIS-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Accurate initial guesses to the solution can dramatically speed convergence of iterative solvers. In the case of successive right hand sides, it has been shown that accurate initial solutions may be obtained by projecting the newest right hand side vector onto a column space of recent prior solutions. We propose a technique to efficiently update the column space of prior solutions. We find this technique can modestly improve solver performance, though its potential is likely limited by the problem step size and the accuracy of the solver.