Abstract
In Chapter 1, we outlined the displacement rank approach (COMPRESS, OPERATE, DECOMPRESS) to computations with structured matrices and in more detail covered its OPERATE stage. In this chapter, we systematically cover the basic techniques required at the COMPRESS and DECOMPRESS stages of this approach. We present these techniques in a unified way but also detail the decompression techniques separately for each of the most popular classes of structured matrices. As an immediate result, we obtain superfast algorithms for multiplying these matrices by vectors and by each other. We accentuate the power of the approach based on the displacement transformations of two kinds that extend successful algorithms from one class of structured matrices to various other classes. We also briefly comment on parallel implementation of computations with structured matrices.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Pan, V.Y. (2001). Structured Matrices and Displacement Operators. In: Structured Matrices and Polynomials. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0129-8_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0129-8_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6625-9
Online ISBN: 978-1-4612-0129-8
eBook Packages: Springer Book Archive