Partitioning sparse matrices with eigenvectors of graphs

A real symmetric matrix of order n has a full set of orthogonal eigenvectors. The most used approach to compute the spectrum of such matrices reduces first the dense symmetric matrix into a symmetric structured one, i.e., tridiagonal matrices or ...

A procedure is presented for finding a number of the smallest eigenvalues and their associated eigenvectors of large sparse Hermitian matrices. The procedure, a modification of an inverse subspace iteration procedure, uses adaptively determined ...

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for $2\times 2$ block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular ...