TMESGEV Compute extreme eigenvectors of a positive-definite Hermitian pencil
SYNOPSIS
function [V,L,stats] = tmesgev(A,B,p,params)
DESCRIPTION
TMESGEV Compute extreme eigenvectors of a positive-definite Hermitian pencil
using the Trace Minimization method of Sameh/Wisniewski and Sameh/Tong
This computes the space corresponding to the smallest eigenvalues of (A,B) by
optimizing the Rayleigh quotient on the Grassman manifold using the Implicit
Riemannian Trust-Region with truncated CG inner solver.
The method uses the TRACEMIN quadratic model:
m_X(eta) = X'*A*X + 2*eta'*A*X + eta'*A*eta
so that rho_X(eta) >= 1.
Manifold points are represented using orthonormal matrices. This is not necessary,
but it simplifies some terms, by removing X'*B*X and inv(X'*B*X).
[V,L] = tmesgev(A,B,p) returns the extreme eigenvectors of rank p.
[V,L,stats] = tmesgev(A,B,p) returns in addition some statistics from the solver.
See RTR for info.
A should be a Hermitian matrix. B should be Hermitian positive-definite or empty.
tmesgev(A,B,p,params) allows the user to specify parameters that are passed
to the RTR solver.
params.x0 - initial iterate (B-orthonormal matrix)
params.epsilon - Outer Convergence tolerance (absolute)
params.useprec - if non-zero, tmesgev will generate a preconditioner for the
problem, based on an incomplete factorization of A.
This requires a positive-definite A.
See also irtresgev, irtr, rtr, rtresgev
