Skip to Main content Skip to Navigation
New interface
Preprints, Working Papers, ...

On the Exponentiation of Interval Matrices

Abstract : The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when dealing with interval matrices exponentiation: Indeed, the main problem will now be the dependency loss of the different occurrences of the variables due to interval evaluation, which may lead to so wide enclosures that they are useless. In this paper, the problem of computing a sharp enclosure of the interval matrix exponential is proved to be NP-hard. Then the scaling and squaring method is adapted to interval matrices and shown to drastically reduce the dependency loss w.r.t. the interval evaluation of the Taylor series.
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00411330
Contributor : Alexandre Goldsztejn Connect in order to contact the contributor
Submitted on : Thursday, August 27, 2009 - 10:34:22 AM
Last modification on : Wednesday, April 27, 2022 - 4:14:57 AM
Long-term archiving on: : Tuesday, June 15, 2010 - 10:50:01 PM

Files

IntervalMatrixExponential.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00411330, version 1
  • ARXIV : 0908.3954

Citation

Alexandre Goldsztejn, Arnold Neumaier. On the Exponentiation of Interval Matrices. 2009. ⟨hal-00411330v1⟩

Share

Metrics

Record views

260

Files downloads

212