The research group develops the theory and algorithms of numerical linear algebra for different number systems, including real, complex, quaternionic, and bicomplex structures. It focuses on efficient methods for solving eigenvalue and singular value problems, QR decompositions, structured matrices, and perturbation theory. The developed algorithms are applied to least-squares problems, image processing and classification, computation of generalized inverses, and finding polynomial roots. Additional research includes operator theory, optimization of damping in oscillatory systems, discrete evolutionary models, and the analysis of symmetric polynomials and their combinatorial applications.

• Generic numerical linear algebra for matrices with entries in one of eight number systems – real numbers, complex numbers, quaternions, reduced bicomplex numbers, and dual numbers derived from the previously listed systems, including:
  • accurate and fast matrix algorithms
  • QR decomposition
  • algorithms for structured matrices
  • perturbation theory for the above problems
• Application of generic algorithms to:
  • least-squares problems
  • image processing and classification
  • computation of generalized inverses
  • computation of polynomial roots
• operator theory
• fast optimization of damping in oscillatory systems
• discrete evolutionary models for periodic organisms
• analysis of symmetric polynomials and their combinatorial interpretations and applications

Laboratories

n/a

Equipment

• Four computers and two workstations

• Synergy of Mathematics and Physics in Engineering (SYMPHA), project IP-UNIST-11, MZOM, principal investigator: Damir Lelas, collaborators: Ivan Slapničar, Nevena Jakovčević Stor, Anita Kujundžić, Petra Marija De Micheli Vitturi, Marija Čatipović, https://www.croris.hr/projekti/projekt/17953?lang=en
• Matrix Algorithms in Noncommutative Associative Algebras (MANAA), project IP-2020-02-2240, Croatian Science Foundation, 2021-2024, principal investigator: Ivan Slapničar, collaborator: Nevena Jakovčević Stor, http://manaa.fesb.unist.hr
• Optimization of Parameter-Dependent Mechanical Systems (OptPDMechSys), project 9540, Croatian Science Foundation, 2015-2019, principal investigator: Ninoslav Truhar, University of Osijek, collaborators: Ivan Slapničar and Nevena Jakovčević Stor
• Fast and Accurate Matrix Algorithms and Applications, project 0023002, Ministry of Science, Education and Sports, 2002-2013, principal investigator: Ivan Slapničar, collaborator: Nevena Jakovčević Stor

Numerical linear algebra, matrix algorithms and applications, image analysis, analysis of symmetric polynomials and their combinatorial interpretations and applications.