A Generalized Limited-Memory BNS Method Based on the Block BFGS Update
Vlček, Jan; Lukšan, Ladislav
2017 - English A block version of the BFGS variable metric update formula is investigated. It satisfies the quasi-Newton conditions with all used difference vectors and gives the best improvement of convergence in some sense for quadratic objective functions, but it does not guarantee that the direction vectors are descent for general functions. To overcome this difficulty and utilize the advantageous properties of the block BFGS update, a block version of the limited-memory BNS method for large scale unconstrained optimization is proposed. The algorithm is globally convergent for convex sufficiently smooth functions and our numerical experiments indicate its efficiency. Keywords: unconstrained minimization; block variable metric methods; limited-memory methods; the BFGS update; global convergence; numerical results Available in digital repository of the ASCR A Generalized Limited-Memory BNS Method Based on the Block BFGS Update

A block version of the BFGS variable metric update formula is investigated. It satisfies the quasi-Newton conditions with all used difference vectors and gives the best improvement of convergence in ...

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2017

The IINC System under the ROOT Environment
Jiřina, Marcel
2017 - English Keywords: IINC; data separation; classification; multivariate data; distance; metric Available in digital repository of the ASCR The IINC System under the ROOT Environment

Jiřina, Marcel
Ústav informatiky, 2017

The use of sequential quadratic programming for solving reachability problems
Kuřátko, Jan
2017 - English Available in digital repository of the ASCR The use of sequential quadratic programming for solving reachability problems

Kuřátko, Jan
Ústav informatiky, 2017

Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization
Vlček, Jan; Lukšan, Ladislav
2017 - English Keywords: unconstrained minimization; block variable metric methods; limited-memory methods; the BFGS update; global convergence; numerical results Available in a digital repository NRGL Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2017

Nondeterministic Computations for Which Space is More Powerful than Time
Wiedermann, Jiří
2016 - English Keywords: nondeterministic computation; crossing sequences; complexity Available in a digital repository NRGL Nondeterministic Computations for Which Space is More Powerful than Time

Wiedermann, Jiří
Ústav informatiky, 2016

A Block Version of the BNS Limited-Memory Variable Metric Method for Unconstrained Minimization
Vlček, Jan; Lukšan, Ladislav
2016 - English Keywords: unconstrained minimization; block variable metric methods; limited-memory methods; the BFGS update; global convergence; numerical results Available in a digital repository NRGL A Block Version of the BNS Limited-Memory Variable Metric Method for Unconstrained Minimization

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2016

Maximum Likelihood Estimation of Diagonal Covariance Matrix
Turčičová, Marie; Mandel, Jan; Eben, Kryštof
2016 - English Keywords: maximum likelihood estimation; parametric model; Fisher information; delta method Available in a digital repository NRGL Maximum Likelihood Estimation of Diagonal Covariance Matrix

Turčičová, Marie; Mandel, Jan; Eben, Kryštof
Ústav informatiky, 2016

Cut Languages in Rational Bases
Šíma, Jiří; Savický, Petr
2016 - English We introduce a so-called cut language which contains the representations of numbers in a rational base that are less than a given threshold. The cut languages can be used to refine the analysis of neural net models between integer and rational weights. We prove a necessary and sufficient condition when a cut language is regular, which is based on the concept of a quasi-periodic power series. We show that any cut language with a rational threshold is context-sensitive while examples of non-context-free cut languages are presented. Keywords: cut language; rational base; quassi-periodic power series Available in a digital repository NRGL Cut Languages in Rational Bases

We introduce a so-called cut language which contains the representations of numbers in a rational base that are less than a given threshold. The cut languages can be used to refine the analysis of ...

Šíma, Jiří; Savický, Petr
Ústav informatiky, 2016

Interval Matrices: Regularity Yields Singularity
Rohn, Jiří
2016 - English It is proved that regularity of an interval matrix implies singularity of two related interval matrices. Keywords: interval matrix; regularity; singularity Available in a digital repository NRGL Interval Matrices: Regularity Yields Singularity

It is proved that regularity of an interval matrix implies singularity of two related interval matrices.

Rohn, Jiří
Ústav informatiky, 2016

On Exact Heteroscedasticity Testing for Robust Regression
Kalina, Jan; Peštová, Barbora
2016 - English The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also the asymptotic behavior of the permutation test statistics of the Goldfeld-Quandt and Breusch-Pagan tests is investigated. A numerical experiment on real economic data is presented, which also shows how to perform a robust prediction model under heteroscedasticity. Keywords: robust estimation; outliers; variance; diagnostic tools; heteroscedasticity Available in digital repository of the ASCR On Exact Heteroscedasticity Testing for Robust Regression

The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also ...

Kalina, Jan; Peštová, Barbora
Ústav informatiky, 2016