Circulants, displacements and decompositions of matrices
I.Gohberg
and
Vadim Olshevsky
New formulas are suggested for the representation
of matrices and their inverses in the form of sums of products of factor
circulants, which are based on the analysis of the factor cyclic
displacement of matrices. The results in applications to Toeplitz matrices
generalize the Gohberg-Semencul, Ben-Artzi-Shalom and Heinig-Rost
formulas and are useful for
complexity analysis.
Related papers:
The formulas, involving factor circulants were used in
[GO94c] to speed-up
matrix-vector multiplication. The displacement equation, involving
circulants, instead of usual shifts, was used in
[GKO95]
to transform Toeplitz-like matrices into Cauchy-like matrices.
Key words:
Displacement structure,
Cyclic displacement,
Toeplitz-like matrices,
Inversion formulas,
Gohberg-Semencul formula,
Gohberg-Krupnik formula,
Heinig-Rost formula,
Ben-Artzi-Shalom formula.
Ammar-Gader formulas.
AMS subject classification:
15A06, 15A09, 15A57
Vadim Olshevsky's Home page
Vadim Olshevsky
olshevsk@isl.stanford.edu
Last modified: Fri Sep 15 1995