TY - JOUR
A1 - Titi, Jihad
A1 - Hamadneh, Tareq
A1 - Garloff, Jürgen
T1 - Convergence of the Simplicial Rational Bernstein Form
JF - Modelling, Computation and Optimization in Information Systems and Management Sciences
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 359)
N2 - Bernstein polynomials on a simplex V are considered. The expansion of a given polynomial p into these polynomials provides bounds for range of p over V. Bounds for the range of a rational function over V can easily be obtained from the Bernstein expansions of the numerator and denominator polynomials of this function. In this paper it is shown that these bounds converge monotonically and linearly to the range of the rational function if the degree of the Bernstein expansion is elevated. If V is subdivided then the convergence is quadratic with respect to the maximum of the diameters of the subsimplices.
KW - Bernstein polynomial
KW - simplex
KW - range bounds
KW - rational function
KW - degree elevation
Y1 - 2015
UR - http://www-home.htwg-konstanz.de/%7Egarloff/Paper95_MCO2015_Titi_Hamadneh_Garloff(1).pdf
U6 - http://dx.doi.org/10.1007/978-3-319-18161-5
SP - 433
EP - 441
ER -
TY - CHAP
A1 - Garloff, Jürgen
A1 - Hamadneh, Tareq
T1 - Convergence and inclusion isotonicity of the tensorial rational Bernstein form
T2 - Scientific Computing, Computer Arithmetic, and Validated Numerics, 16th International Symposium, SCAN 2014, Würzburg, Germany, September 21-26, 2014, (Lecture Notes in Computer Science ; 9553)
N2 - A method is investigated by which tight bounds on the range of a multivariate rational function over a box can be computed. The approach relies on the expansion of the numerator and denominator polynomials in Bernstein polynomials. Convergence of the bounds to the range with respect to degree elevation of the Bernstein expansion, to the width of the box and to subdivision are proven and the inclusion isotonicity of the related enclosure function is shown.
KW - Bernstein polynomial
KW - Rational function
KW - Range bounding
Y1 - 2016
SN - 978-3-319-31768-7
U6 - http://dx.doi.org/10.1007/978-3-319-31769-4
N1 - Volltextzugriff für Angehörige der Hochschule Konstanz möglich.
SP - 171
EP - 179
PB - Springer
CY - Cham
ER -
TY - CHAP
A1 - Titi, Jihad
A1 - Garloff, Jürgen
T1 - Enclosure of the Range of a Complex Polynomial Over a Complex Interval
T2 - Sixth Palestinian Conference on Modern Trends in Mathematics and Physics (PCMTMP-VI), 5. - 8. August 2018, Palestine Technical University Kadoorei, Palästina
KW - Range enclosure
KW - Complex polynomial
KW - Complex interval
KW - Bernstein polynomial
Y1 - 2018
ER -
TY - CHAP
A1 - Titi, Jihad
A1 - Garloff, Jürgen
T1 - Enclosure of the Range of a Complex Polynomial Over a Complex Interval
T2 - SCAN 2018, The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations, 10 - 15 September 2018, Waseda University, Tokyo, Japan
KW - Complex interval
KW - Complex polynomial
KW - Enclosure of the range
KW - Bernstein polynomial
KW - Multivariate complex polynomial
Y1 - 2018
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bsz:kon4-opus4-14627
SP - 40
EP - 41
PB - Waseda University
CY - Tokyo, Japan
ER -