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National Repository of Grey Literature 3 records found  Search took 0.02 seconds. 
Properties and construction of core problem in data fitting problems with multiple observations
 Dvořák, Jan ; Hnětynková, Iveta (advisor) ; Plešinger, Martin (referee)
In this work we study the solution of linear approximation problems with multiple observations. Particulary we focus on the total least squares method, which belogs to the class of ortogonaly invariant problems. For these problems we describe the so called core reduction. The aim is to reduce dimesions of the problem while preserving the solution, if it exists. We present two ways of constructing core problems. One is based on the singular value decomposition and the other uses the generalized Golub-Kahan iterative bidiago- nalization. Further we investigate properties of the core problem and of the methods for its construction. Finally we preform numerical experiments in the Matlab enviroment in order to test the reliability of the discussed algorithms. 1
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Behavior of total least squares method for models with multiple observations
 Slavenko, Matvei ; Hnětynková, Iveta (advisor) ; Tůma, Miroslav (referee)
Linear approximation problems arise in various applications and can be solved by a large variety of methods. One of such methods is total least squares (TLS), an approach that allows to correct errors both in the linear model and available set of observations. In this work we collect and compare the main theoretical results related to TLS with multiple right-hand side. Particularly we describe the classification of TLS problems and summarise the solvability analysis that has currently been spread over various sources. The second part of the work is dedicated to an approach called core data reduction (CDR) and proof-of-concept programme demonstrating the CDR numerical behaviour. 1
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Global krylov methods for solving linear algebraic problems with matrix observations
 Rapavý, Martin ; Hnětynková, Iveta (advisor) ; Tichý, Petr (referee)
In this thesis we study methods for solving systems of linear algebraic equati- ons with multiple right hand sides. Specifically we focus on block Krylov subspace methods and global Krylov subspace methods, which can be derived by various approaches to generalization of methods GMRES and LSQR for solving systems of linear equations with single right hand side. We describe the difference in construction of orthonormal basis in block methods and F-orthonormal basis in global methods, in detail. Finally, we provide numerical experiments for the deri- ved algorithms in MATLAB enviroment. On carefully selected test problems we compare convergence properties of the methods. 1
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