Speaker
Description
The BiCG method for solving linear equations has a polynomial at its core. The new Twin BiCG method solves multiple right-hand systems using the same polynomial for each system. This polynomial is applied implicitly by using the parameters from solving the first right-hand side for all of the systems. Twin BiCG has automatic stability control from the extra copies of eigenvalues that are produced by the nonsymmetric Lanczos algorithm.
We also discuss how Twin BiCG can give an approximation to the inverse of a matrix. Applications include Multilevel Monte Carlo for determining the trace of the inverse of a large matrix. Also, shift-and-invert Arnoldi for computing eigenvalues can solve the associated linear equations to less accuracy as the iteration proceeds. Twin BiCG can efficiently implement this.