Locally Optimal Block Preconditioned Conjugate Gradient method

Prof. Andrew Knyazev Ph.D. M.Sc.

Sept. 5, 2005, 2 p.m. HF 136

We present the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for symmetric eigenvalue problems and discuss its implementation in the software package Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX). The LOBPCG method, suggested and developed by Andrew Knyazev [1] in the past decade, recently attracts an increasing attention as a potential alternative to the shift-and-invert Lanczos and preconditioned Davidson methods due to its simplicity robustness and fast convergence. Several MATLAB, C, C++ and FORTRAN implementations of the LOBPCG are developed by different groups, e. g., for such applications areas as electromagnetics, structured mechanics and electronic structure calculations.

[1] A.V. Knyazev, "Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method."
SIAM Journal on Scientific Computing 23 (2001), no. 2, pp. 517-541.