Reduces a real, symmetric matrix to tridiagonal form, using Householder’s method.

a—An n-by-n real, symmetric matrix.

a—This input parameter is replaced, on output, by the orthogonal matrix Q, effecting the transformation. The TQLI procedure uses this result to find the eigenvectors of the matrix A.

d—(optional) An n-element vector containing the diagonal elements of the tridiagonal matrix.

e—(optional) An n-element vector containing the off-diagonal elements of the tridiagonal matrix.

None.

TQLI

TRED2 is based on a routine of the same name in Numerical Recipes in C: The Art of Scientific Computing, by Flannery, Press, Teukolsky, and Vetterling, Cambridge University Press, Cambridge, MA, 1988. It is used by permission.