Sharpening the triple diagonal form

Let R be a Euclidean domain with quotient field F of characteristic not equaling 2. Jacobi showed that every symmetric R-matrix is congruent over R to a matrix in triple diagonal form. Since it is generally not possible to fully diagonalize these matrices, it is of importance to gain as much control as possible of this triple diagonal form. This paper focuses on controlling the off-diagonal elements. (C) 2010 Elsevier Inc. All rights reserved.