Organization of a ``Fixed-Plus-Variable'' Structure Computer for Computation of Eigenvalues and Eigenvectors of Real Symmetric Matrices

This paper presents a new procedure to compute many or all of the eigenvalues and eigenvectors of symmetric Toeplitz matrices. The key to this algorithm is the use of the ''Shift-and-Invert'' technique applied with iterative methods, which allows the ...

Among hollow, symmetric $n$-by-$n$ nonnegative matrices, it is shown that any number $k$, $2\leq k\leq n-1$ of nonpositive eigenvalues is possible. However, as $n$ grows, small numbers of nonpositive eigenvalues become increasingly rare. In particular, if ...

We consider the class of totally nonnegative (TN) matrices---matrices all of whose minors are nonnegative. Any nonsingular TN matrix factors as a product of nonnegative bidiagonal matrices. The entries of the bidiagonal factors parameterize the set of ...