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MAT TRIAD 2019: Book of Abstracts
Bok, J.; Hartman, David; Hladík, M.; Rozložník, Miroslav
2019 - anglický
This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers in a variety of aspects of matrix analysis and its interdisciplinary applications to meet and share interests and ideas. The conference topics include matrix and operator theory and computation, spectral problems, applications of linear algebra in statistics, statistical models, matrices and graphs as well as combinatorial matrix theory and others. The goal of this event is to encourage further growth of matrix analysis research including its possible extension to other fields and domains. Klíčová slova: proceedings; conference; matrix analysis Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
MAT TRIAD 2019: Book of Abstracts

This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers ...

Bok, J.; Hartman, David; Hladík, M.; Rozložník, Miroslav
Ústav informatiky, 2019

Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství
Rohn, Jiří
2019 - český
V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. Bouška, J. Rohn a B. Kalendovský). Klíčová slova: Leontěvův model; intervalová data; zaručené řešení; neexistence; matice 28 x 28 Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství

V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. ...

Rohn, Jiří
Ústav informatiky, 2019

Absolute Value Mapping
Rohn, Jiří
2019 - anglický
We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for each right-hand side. Klíčová slova: absolute value mapping; bijectivity; interval matrix; regularity; absolute value equation; unique solvability Plné texty jsou dostupné v digitálním repozitáři NUŠL
Absolute Value Mapping

We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for ...

Rohn, Jiří
Ústav informatiky, 2019

A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix
Lukšan, Ladislav; Vlček, Jan
2019 - anglický
In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, such that AT f = JT f. This property allows us to solve a linear least squares problem, minimizing ∥Ad+f∥ instead of solving the normal equation ATAd+JT f = 0, where d ∈ Rn is the required direction vector. Computational experiments confirm the efficiency of the new method. Klíčová slova: nonlinear least squares; hybrid methods; trust-region methods; quasi-Newton methods; numerical algorithms; numerical experiments Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix

In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, ...

Lukšan, Ladislav; Vlček, Jan
Ústav informatiky, 2019

On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle
Matonoha, Ctirad; Papáček, Š.
2019 - anglický
This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of fluorescent particle concentration, see [6, 1, 3, 4, 5]. More precisely, we continue to look for an optimal bleaching pattern used in FRAP (Fluorescence Recovery After Photobleaching), being the initial condition of the Fickian diffusion equation maximizing a sensitivity measure. As follows, we define an optimization problem and we show the special feature (so-called complementarity principle) of the optimal binary-valued initial conditions. Klíčová slova: parameter identification; bleaching pattern; initial boundary value problem; sensitivity measure Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle

This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of ...

Matonoha, Ctirad; Papáček, Š.
Ústav informatiky, 2019

Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR
Šebesta, Václav
2019 - český
Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR Plné texty jsou dostupné v digitálním repozitáři NUŠL
Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR

Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR

Šebesta, Václav
Ústav informatiky, 2019

Overdetermined Absolute Value Equations
Rohn, Jiří
2019 - anglický
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case. Klíčová slova: absolute value equations; overdetermined system Plné texty jsou dostupné v digitálním repozitáři NUŠL
Overdetermined Absolute Value Equations

We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.

Rohn, Jiří
Ústav informatiky, 2019

Generalization of a Theorem on Eigenvalues of Symmetric Matrices
Rohn, Jiří
2019 - anglický
We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real. Klíčová slova: symmetric matrix; positive semide nite matrix; real spectrum Plné texty jsou dostupné v digitálním repozitáři NUŠL
Generalization of a Theorem on Eigenvalues of Symmetric Matrices

We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real.

Rohn, Jiří
Ústav informatiky, 2019

Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods
Vlček, Jan; Lukšan, Ladislav
2019 - anglický
To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time. The limit update is a block BFGS update. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method. Klíčová slova: unconstrained minimization; limited-memory variable metric methods; the repeated Byrd-Nocedal-Schnabel update; the Lyapunov matrix equation; the conjugate directions; global convergence; numerical results Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods

To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed. Since this can be time consuming, the extra updates need to be ...

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2019

Hybrid Methods for Nonlinear Least Squares Problems
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
2019 - anglický
This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with extensive computational tests and comparisons of the introduced methods. All hybrid methods are described in detail and their global convergence is proved in a unified way. Some proofs concerning trust region methods, which are difficult to find in the literature, are also added. In particular, the report contains an analysis of a new simple hybrid method with Jacobian corrections (Section 8) and an investigation of the simple hybrid method for sparse least squares problems proposed previously in [33] (Section 14). Klíčová slova: numerical optimization; nonlinear least squares; trust region methods; hybrid methods; sparse problems; partially separable problems; numerical experiments Plné texty jsou dostupné v digitálním repozitáři NUŠL
Hybrid Methods for Nonlinear Least Squares Problems

This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with ...

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
Ústav informatiky, 2019

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