Number of found documents: 771
Published from to

Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
Gergelits, Tomáš; Mardal, K.-A.; Nielsen, B. F.; Strakoš, Z.
2019 - English
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. Keywords: second order elliptic PDEs; preconditioning by the inverse Laplacian; eigenvalues of the discretized preconditioned problem; nodal values of the coefficient function; Hall’s theorem; convergence of the conjugate gradient method Available in digital repository of the ASCR
Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator

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 ...

Gergelits, Tomáš; Mardal, K.-A.; Nielsen, B. F.; Strakoš, Z.
Ústav informatiky, 2019

A Nonparametric Bootstrap Comparison of Variances of Robust Regression Estimators.
Kalina, Jan; Tobišková, N.; Tichavský, J.
2019 - English
While various robust regression estimators are available for the standard linear regression model, performance comparisons of individual robust estimators over real or simulated datasets seem to be still lacking. In general, a reliable robust estimator of regression parameters should be consistent and at the same time should have a relatively small variability, i.e. the variances of individual regression parameters should be small. The aim of this paper is to compare the variability of S-estimators, MM-estimators, least trimmed squares, and least weighted squares estimators. While they all are consistent under general assumptions, the asymptotic covariance matrix of the least weighted squares remains infeasible, because the only available formula for its computation depends on the unknown random errors. Thus, we take resort to a nonparametric bootstrap comparison of variability of different robust regression estimators. It turns out that the best results are obtained either with MM-estimators, or with the least weighted squares with suitable weights; the latter estimator is especially recommendable for small sample sizes. Keywords: robustness; linear regression; outliers; bootstrap; least weighted squares Fulltext is available at external website.
A Nonparametric Bootstrap Comparison of Variances of Robust Regression Estimators.

While various robust regression estimators are available for the standard linear regression model, performance comparisons of individual robust estimators over real or simulated datasets seem to be ...

Kalina, Jan; Tobišková, N.; Tichavský, J.
Ústav informatiky, 2019

Implicitly weighted robust estimation of quantiles in linear regression
Kalina, Jan; Vidnerová, Petra
2019 - English
Estimation of quantiles represents a very important task in econometric regression modeling, while the standard regression quantiles machinery is well developed as well as popular with a large number of econometric applications. Although regression quantiles are commonly known as robust tools, they are vulnerable to the presence of leverage points in the data. We propose here a novel approach for the linear regression based on a specific version of the least weighted squares estimator, together with an additional estimator based only on observations between two different novel quantiles. The new methods are conceptually simple and comprehensible. Without the ambition to derive theoretical properties of the novel methods, numerical computations reveal them to perform comparably to standard regression quantiles, if the data are not contaminated by outliers. Moreover, the new methods seem much more robust on a simulated dataset with severe leverage points. Keywords: regression quantiles; robust regression; outliers; leverage points Fulltext is available at external website.
Implicitly weighted robust estimation of quantiles in linear regression

Estimation of quantiles represents a very important task in econometric regression modeling, while the standard regression quantiles machinery is well developed as well as popular with a large number ...

Kalina, Jan; Vidnerová, Petra
Ústav informatiky, 2019

A Logical Characteristic of Read-Once Branching Programs
Žák, Stanislav
2019 - English
We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two appropriate properties: i) The ”knowledge” arising at a stage of computation in question is derivable from the ”knowledge” arising at the previous stage according to the rules of the model and according to the local arrangement of the b.p. ii) The model confirms the intuitively well-known fact that the knowledge arising at a node of a computation depends not only on it but in some cases also on a ”mystery” information. (I. e. different computations reaching the same node may have different knowledge(s) arisen at it.) We prove that with respect to our model no such information exists in read-once b.p.‘s but on the other hand in b. p.‘s which are not read-once such information must be present. The read-once property forms a frontier. More concretely, we may see the instances of our models as a systems S = (U,D) where U is a universe of knowledge and D are derivation rules. We say that a b.p. P is compatible with a system S iff along each computation in P S derives F (false) or T (true) at the end correctly according to the label of the reached sink. This key notion modifies the classic paradigm which takes the computational complexity with respect to different classes of restricted b.p.‘s (e.g. read-once b.p.‘s, k-b.p.‘s, b.p.‘s computing in limited time etc.). Now, the restriction is defined by a subset of systems and only these programs are taken into account which are compatible with at least one of the chosen systems. Further we understand the sets U of knowledge(s) as a sets of admissible logical formulae. It is clear that more rich sets U‘s imply the large restrictions on b.p.‘s and consequently the smaller complexities of Boolean functions are detected. More rich logical equipment implies stronger computational effectiveness. Another question arises: given a set of Boolean functions (e.g. codes of some graphs) what logical equipment is optimal from the point of complexity? Keywords: branching programs; computational complexity; logic Available in digital repository of the ASCR
A Logical Characteristic of Read-Once Branching Programs

We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two ...

Žák, Stanislav
Ústav informatiky, 2019

Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství
Rohn, Jiří
2019 - Czech
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). Keywords: Leontěvův model; intervalová data; zaručené řešení; neexistence; matice 28 x 28 Available in digital repository of the ASCR
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 - English
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. Keywords: absolute value mapping; bijectivity; interval matrix; regularity; absolute value equation; unique solvability Available in a digital repository NRGL
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

Overdetermined Absolute Value Equations
Rohn, Jiří
2019 - English
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case. Keywords: absolute value equations; overdetermined system Available in a digital repository NRGL
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

On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle
Matonoha, Ctirad; Papáček, Š.
2019 - English
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. Available in digital repository of the ASCR
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

Generalization of a Theorem on Eigenvalues of Symmetric Matrices
Rohn, Jiří
2019 - English
We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real. Keywords: symmetric matrix; positive semide nite matrix; real spectrum Available in a digital repository NRGL
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

Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?
Rohn, Jiří
2019 - English
We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is generally not valid, and we prove that it becomes true under an additional assumption of positive semide niteness of the midpoint matrix. The proof is constructive. Keywords: symmetric interval matrix; singularity; positive semide niteness Available in a digital repository NRGL
Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?

We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is ...

Rohn, Jiří
Ústav informatiky, 2019

About project

NRGL provides central access to information on grey literature produced in the Czech Republic in the fields of science, research and education. You can find more information about grey literature and NRGL at service web

Send your suggestions and comments to nusl@techlib.cz

Provider

http://www.techlib.cz

Facebook

Other bases