Department of Computer Science, K.U.Leuven, Leuven, Belgium
TW Reports vol:TW368
In this paper the deﬁnition of semiseparable matrices is invest-
igated. Properties of the frequently used deﬁnition and the corres-
ponding representation by generators are deduced. Corresponding
to the class of tridiagonal matrices another deﬁnition of semisepar-
able matrices is introduced preserving the nice properties dual to
the class of tridiagonal matrices. Several theorems and properties
are included showing the viability of this alternative deﬁnition.
Because of the alternative deﬁnition, the standard representation
of semiseparable matrices is not satisfying anymore. The concept of
a representation is explicitely formulated and a new kind of repres-
entation corresponding to the alternative deﬁnition is given. It is
proved that this representation keeps all the interesting properties
of the generator representation.
As an example of the eﬀectivity of the new representation, we
design on O(n) algorithm for the multiplication of a semiseparable
matrix given by the new representation, with a vector.