Skip to main content Accessibility help
×
×
Home

Using randomization to make recursive matrix algorithms practical

  • DINH LÊ (a1) and D. STOTT PARKER (a1)
    • Published online: 01 November 1999
Abstract

Recursive block decomposition algorithms (also known as quadtree algorithms when the blocks are all square) have been proposed to solve well-known problems such as matrix addition, multiplication, inversion, determinant computation, block LDU decomposition and Cholesky and QR factorization. Until now, such algorithms have been seen as impractical, since they require leading submatrices of the input matrix to be invertible (which is rarely guaranteed). We show how to randomize an input matrix to guarantee that submatrices meet these requirements, and to make recursive block decomposition methods practical on well-conditioned input matrices. The resulting algorithms are elegant, and we show the recursive programs can perform well for both dense and sparse matrices, although with randomization dense computations seem most practical. By ‘homogenizing’ the input, randomization provides a way to avoid degeneracy in numerical problems that permits simple recursive quadtree algorithms to solve these problems.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Functional Programming
  • ISSN: 0956-7968
  • EISSN: 1469-7653
  • URL: /core/journals/journal-of-functional-programming
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed

Using randomization to make recursive matrix algorithms practical

  • DINH LÊ (a1) and D. STOTT PARKER (a1)
    • Published online: 01 November 1999
Submit a response

Discussions

No Discussions have been published for this article.

×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *