Type of Publication:  Contribution to a conference collection 
Author:  Garloff, Jürgen 
Year of publication:  2011 
Conference:  3rd Conference of Mathematical Sciences, Apr 27, 2011  Apr 28, 2011, Zarqa, Jordanien 
Published in:  Proceedings of the 3rd Conference of Mathematical Sciences : CMS 2011, 2728 April 2011, Zarqa, Jordanien / Jaber, Khalid (ed.).  Zarqa : Zarqa University, 2011.  pp. 21372156 
DOI (citable link):  https://dx.doi.org/10.1007/s0060701101597 
Summary: 
The paper considers systems of linear interval equations, i. e., linear systems where the coefficients of the matrix and the right hand side vary between given bounds. We consider direct methods for the enclosure of the solution set of such a system. The algorithms are obtained from the ordinary elimination procedures by replacing the real numbers by the related intervals and the real operations by the respective interval operations. We report on methods by which the breakdown of the interval variants of the Gaussian elimination and the Neville elimination caused by division of an interval containing zero can be avoided for some classes of matrices with identically signed inverses. These include the nonsingular totally nonnegative matrices. The approach consists of a tightening of the interval pivot by determining the exact range of the pivot over the matrix interval. By means of the interval Cholesky method an enclosure of the solution set for symmetric matrices can be found. We present a method by which the diagonal entries of the interval Cholesky factor can be tightened for positive definite interval matrices, such that a breakdown of the algorithm can be prevented. In the case of positive definite symmetric Toeplitz matrices, a further tightening of the interval pivots and other entries of the Cholesky factor is possible.

Subject (DDC):  510 Mathematics 
Keywords:  Interval Neville elimination, interval Cholesky method, totally nonnegative matrix, positive definite matrix, Toeplitz matrix 
Bibliography of Konstanz:  Yes 
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GARLOFF, Jürgen, 2011. Pivot tightening for some direct methods for solving systems of linear interval equations. 3rd Conference of Mathematical Sciences. Zarqa, Jordanien, Apr 27, 2011  Apr 28, 2011. In: JABER, Khalid, ed.. Proceedings of the 3rd Conference of Mathematical Sciences : CMS 2011, 2728 April 2011, Zarqa, Jordanien. Zarqa:Zarqa University, pp. 21372156. Available under: doi: 10.1007/s0060701101597
@inproceedings{Garloff2011Pivot18703, title={Pivot tightening for some direct methods for solving systems of linear interval equations}, year={2011}, doi={10.1007/s0060701101597}, address={Zarqa}, publisher={Zarqa University}, booktitle={Proceedings of the 3rd Conference of Mathematical Sciences : CMS 2011, 2728 April 2011, Zarqa, Jordanien}, pages={21372156}, editor={Jaber, Khalid}, author={Garloff, Jürgen} }
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