Folded spectrum method

The term Folded Spectrum Method (FSM ) or spectrum denotes convolution, a mathematical iterative optimization method for eigenvalue problems. With it, it is possible to determine the eigenvector of a large eigenvalue problem to the matrix that is closest to a desired target natural value (from the center of the spectrum), without having to remove the entire matrix.

Formula

, And with the identity matrix.

Assessment

In contrast to the climber algorithm (english hill climbing, and downhill ) or the CG method, the gradient here (FSM ) is determined by twice applying the matrix:

This method is especially suitable for large sparse matrices.