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# EPSLOBPCG

EPSLOBPCG = “lobpcg” - The Locally Optimal Block Preconditioned Conjugate Gradient method.

## Notes

This is a preconditioned eigensolver, that is, a preconditioner can be used to accelerate convergence, but as opposed to Davidson methods it is intended for computing leftmost eigenvalues of Hermitian problems, and not interior eigenvalues.

The implemented method is LOBPCG [Knyazev, 2001]. Note that SLEPc provides another implementation of LOBPCG via BLOPEX, see `EPSBLOPEX`.

The preconditioner is specified via the internal `ST` object and its associated `KSP`.

## References

[Kny01]

A. V. Knyazev. Toward the optimal preconditioned eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient method. SIAM J. Sci. Comput., 23(2):517–541, 2001. doi:10.1137/S1064827500366124.

## See Also

EPS: Eigenvalue Problem Solver, `EPS`, `EPSType`, `EPSSetType()`, `EPSGetST()`, `EPSBLOPEX`

## Level

beginner

## Location

src/eps/impls/cg/lobpcg/lobpcg.c

Index of all EPS routines Table of Contents for all manual pages Index of all manual pages