TY - JOUR
T1 - Using interval unions to solve linear systems of equations with uncertainties
AU - Montanher, Tiago de Morais
AU - Domes, Ferenc
AU - Schichl, Hermann
AU - Neumaier, Arnold
PY - 2017/9
Y1 - 2017/9
N2 - An interval union is a finite set of closed and disjoint intervals. In this paper we introduce the interval union Gauss–Seidel procedure to rigorously enclose the solution set of linear systems with uncertainties given by intervals or interval unions. We also present the interval union midpoint and Gauss–Jordan preconditioners. The Gauss–Jordan preconditioner is used in a mixed strategy to improve the quality and efficiency of the algorithm. Numerical experiments on interval linear systems generated at random show the capabilities of our approach.
AB - An interval union is a finite set of closed and disjoint intervals. In this paper we introduce the interval union Gauss–Seidel procedure to rigorously enclose the solution set of linear systems with uncertainties given by intervals or interval unions. We also present the interval union midpoint and Gauss–Jordan preconditioners. The Gauss–Jordan preconditioner is used in a mixed strategy to improve the quality and efficiency of the algorithm. Numerical experiments on interval linear systems generated at random show the capabilities of our approach.
KW - Interval union arithmetic
KW - Interval union Gauss–Seidel
KW - Interval union linear systems
KW - Rigorous numerical linear algebra
UR - http://www.scopus.com/inward/record.url?scp=85018832419&partnerID=8YFLogxK
U2 - 10.1007/s10543-017-0657-x
DO - 10.1007/s10543-017-0657-x
M3 - Article
SN - 0006-3835
VL - 57
SP - 901
EP - 926
JO - BIT Numerical Mathematics
JF - BIT Numerical Mathematics
IS - 3
ER -