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##

The Lanczos-Ritz values appearing in a reduction to an
upper triangular semiseparable matrix

We know from the reduction algorithm as presented in Theorem 51, that the intermediate matrices , have the upper
matrix of upper triangular semiseparable form. Using the
relations provided in Theorem 58, we know that the
singular values of this matrix are the square roots of the
eigenvalues of the matrix
, and the eigenvalues
of the matrix
as can be seen when combining Theorem 58 and the results from Section 5.2.1 are the
Lanczos-Ritz values.

Raf Vandebril
2004-05-03