Title: A note on the representation and definition of semiseparable matrices
Authors: Vandebril, Raf
Van Barel, Marc
Mastronardi, Nicola
Issue Date: Oct-2003
Publisher: Department of Computer Science, K.U.Leuven, Leuven, Belgium
Series Title: TW Reports vol:TW368
Abstract: 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.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Numerical Analysis and Applied Mathematics Section
Electrical Engineering - miscellaneous

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