Department of Computer Science, K.U.Leuven, Leuven, Belgium
TW Reports vol:TW355 pages:20
It is well known how any symmetric matrix can be reduced by
an orthogonal similarity transformation into tridiagonal form. Once
the tridiagonal matrix has been computed, several algorithms can
be used to compute either the whole spectrum or part of it. In this
paper, we propose an algorithm to reduce any symmetric matrix into
a similar semiseparable one of semiseparability rank 1, by orthogonal
similarity transformations. A remarkable feature of the algorithm is
that, after few steps of it, the largest eigenvalues, in absolute value,
are already computed with high precision.
Once the semiseparable matrix has been computed, to compute
the whole spectrum either the same algorithm can be iterated or
algorithms for computing the eigendecomposition of diagonal plus
semiseparable matrices, available in the literature, can be used.
These features of the proposed algorithm are conﬁrmed by some