 

Hybrid Methods for Nonlinear Least Squares Problems
Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan
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).
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Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to LimitedMemory Optimization Methods
Vlček, Jan ; Lukšan, Ladislav
To improve the performance of the LBFGS 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.


Absolute Value Mapping
Rohn, Jiří
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 righthand side.
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The scalarvalued score functions of continuous probability distribution
Fabián, Zdeněk
In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not the observed value, which is to be used in probabilistic and statistical considerations, but its 'treated form', the value of the scalarvalued score function of distribution of the assumed model. Actually, the opinion that an observed value of random variable should be 'treated' with respect to underlying model is one of main ideas of the inference based on likelihood in classical statistics. However, a vector nature of Fisher score functions of classical statistics does not enable a consistent use of this point of view. Instead, various inference functions are suggested and used in solutions of various statistical problems. Inference function of this report is the scalarvalued score function of distribution.


Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
Gergelits, Tomáš ; Mardal, K.A. ; Nielsen, B. F. ; Strakoš, Z.
This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatiotemporal 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 (socalled complementarity principle) of the optimal binaryvalued initial conditions.


On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation  a Complementarity Principle
Matonoha, Ctirad ; Papáček, Š.
This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatiotemporal 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 (socalled complementarity principle) of the optimal binaryvalued initial conditions.


Vulnerability analysis of climate change impacts in the city of Prague
Lorencová, Eliška ; Emmer, Adam ; Geletič, Jan ; Vačkář, David
Climate change is one of the key challenges of the 21st century, both in terms of adaptation as well as mitigation. The aim of this research was, following the Adaptation Strategy of the City of Prague, to prepare the background analysis for the Adaptation Action Plan, focusing on vulnerability assessment. The vulnerability asssessment focused on the climate change impacts related to: (i) temperature extremes  heatwaves, (ii) insufficient rainwater retention and extreme rainfall. The approach included spatiallyspecific analysis using ArcGIS based on climatic, land use and socioeconomic indicators for the current status and future RCP 4.5 and RCP 8.5 scenarios. Regarding vulnerability to heatwaves, the most affected areas are located in the city center (Prague 2, Prague 3, Prague 6, Prague 7, Prague 1) and some peripheral areas with industrial buildings (e.g. Libeň or Štěrboholy). Vulnerability to extreme precipitation and insufficient rainwater retention was highest particularly at the confluence of the Vltava and Berounka (Velká Chuchle, Prague 16, Zbraslav and Lipence).


Web Disinformation Detection  Case Study  Novicok in Czechia
Řimnáč, Martin
The paper presents a case study of the propaganda usage on a real cause of double agent Sergei Skripal. The formal model describing statements published in web articles is announced and particular interesting aspects of used disinformation are provided together with the reasons, why the disinformation is published. The paper is aimed at the presentation of the data collection to have been created and provides a brief discussion on the used propaganda techniques.
