An absolute masterwork – essential for any serious numerical linear algebra researcher. Not for the faint-hearted, but immensely rewarding. Keep it on your shelf next to Wilkinson and Golub & Van Loan.

The Symmetric Eigenvalue Problem | SIAM Publications Library

cover the “direct” methods that transform ( A ) into tridiagonal form using orthogonal matrices (Householder or Givens rotations). Topics include:

Parlett also discusses the software packages available for solving the symmetric eigenvalue problem, including:

The book is highly regarded for its "lively" commentary and expert judgment on the "art" of computing eigenvalues for real symmetric matrices. Google Books Core Focus and Structure

complexity for computing all eigenvectors of a tridiagonal matrix. Availability and Further Reading