Decompositions and Approximations of Matrices and Tensors

Installation Research Project funded by Croatian science foundation Code: 2019045200 Duration: January 2020  December 2024 (60 months) Total value: 1.007.800,00 HRK Contact: ebegovic [at] fkit.hr 
AboutThe most important and the most challenging problems of the scientific computing are those involving very big amount of numerical data modelled by big matrices or multidimensional tensors. Limitations of the computer memory and the fact that we want to obtain the solution fast imply additional requirements to our problems. We can overcome these obstacles by wellcreated algorithms that efficiently use computer memory while keeping the relative accuracy. Some of the approaches in this direction are using the particular structure of the problem in question, using lowrank approximations of matrices or tensors, and using matrix or tensor decompositions. Our group works on hot topics of numerical linear algebra where many interesting questions are raised, both theoretical ones and those involving various applications. Proposed research can be split into the following six sections: (1) Numerical algorithms for tensors, (2) Structurepreserving matrix and tensor approximations, (3) Algorithms for the nonlinear eigenvalue problem, (4) Applications of matrix decompositions in ultrasound tomography, (5) Jacobitype methods for the eigenvalue problem, and (6) Coupled decompositions. Keywords: numerical linear algebra, scientific computing, factorization, aproximation, eigendecomposition, structurepreserving algorithms 
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