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Projects / Programmes source: ARIS

Geometric interpolation and geometric integration

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Research activity

Code Science Field Subfield
1.01.00  Natural sciences and mathematics  Mathematics   

Code Science Field
P170  Natural sciences and mathematics  Computer science, numerical analysis, systems, control 
Keywords
geometric interpolation, approximation, parametric curve, parametric surface, geometric integration, Lie groups, Magnus method
Evaluation (rules)
source: COBISS
Evaluation of bibliographic research performance indicators according to ARIS methodology
Citations Citations for bibliographic records in COBIB.SI that are linked to records in citation databases
source: WoS source: Scopus source: COBISS
Researchers (5)
no. Code Name and surname Research area Role Period No. of publications
1.  02506  MSc Andrej Kmet  Mathematics  Researcher  2003 - 2005  99 
2.  03425  PhD Jernej Kozak  Mathematics  Researcher  2003 - 2005  296 
3.  03533  PhD Mitja Lakner  Mathematics  Researcher  2003 - 2005  115 
4.  09634  PhD Bojan Orel  Mathematics  Head  2003 - 2005  124 
5.  19886  PhD Emil Žagar  Mathematics  Researcher  2003 - 2005  186 
Organisations (1)
no. Code Research organisation City Registration number No. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,223 
Abstract
One part of the proposed project will be interested in geometric interpolation by (piecewise) polynomial parametric curves and surfaces. Geometric interpolation, as a new way of interpolation, has been developed in late eighties and became more and more popular later on. It provides higher order accuracy approximation schemes and preserves geometric properties independently of parametrisation. Applications of the obtained schemes can be found in such important branches as computer design and computer modeling are. Our work will be focused on geometric interpolation of curve data in several dimensions, and on interpolation of surfaces by parametric polynomial patches of different types. The focus of the second part of the proposed research project is solution of differential equations by numerical methods that retain qualitative features of the underlying mathematical structure. The new approach, known as geometric integration, brings together the ideas from traditional numerical analysis, differential topology, theory of Lie groups and nonlinear dynamical systems. In this framework we will develop error estimates for Lie group methods.
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