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1842. An introduction to hierarchical matrices
- Creator:
- Hackbusch, Wolfgang, Grasedyck, Lars, and Börm, Steffen
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- hierarchical matrices, data-sparse approximations, formatted matrix operations, and fast solvers
- Language:
- English
- Description:
- We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short H-matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrixmatrix multiplication, addition and inversion) can be performed in, up to logarithmic factors, optimal complexity.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1843. An iteration process for nonlinear mappings in uniformly convex linear metric spaces
- Creator:
- Beg, Ismat
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- linear metric space, fixed point, and uniformly convex
- Language:
- English
- Description:
- We obtain necessary conditions for convergence of the Cauchy Picard sequence of iterations for Tricomi mappings defined on a uniformly convex linear complete metric space.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1844. An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form
- Creator:
- Szabö, Peter
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- max-plus algebra, eigenvalue, sub-partition of an integer, and Toeplitz matrix
- Language:
- English
- Description:
- The paper presents an iterative algorithm for computing the maximum cycle mean (or eigenvalue) of n×n triangular Toeplitz matrix in max-plus algebra. The problem is solved by an iterative algorithm which is applied to special cycles. These cycles of triangular Toeplitz matrices are characterized by sub-partitions of n−1.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1845. An iterative algorithm for testing solvability of max-min interval systems
- Creator:
- Myšková, Helena
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- max-min algebra, interval system, T4-vector, T4 solvability, T5-vector, and T5 solvability
- Language:
- English
- Description:
- This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the algebraic structure in which classical addition and multiplication are replaced by ⊕ and \kr, where a⊕b=max{a,b},a\krb=min{a,b}. The notation \mbfA\krx=\mbfb represents an interval system of linear equations, where \mbfA=[\pA,\nA] and \mbfb=[\pb,\nb] are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 and T5 solvability and give necessary and sufficient conditions for them.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1846. An object-oriented overland flow solver for watershed flood inundation predictions: case study of Ulus basin, Turkey
- Creator:
- Turan, Burak and Wang, Keh-Han
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- flood inundation, dam break, finite volume, wet/dry, hydrograph, and object oriented programming
- Language:
- Slovak
- Description:
- This paper presents an object-oriented two-dimensional (2-D) overland flow model and its application in simulating flood flows over Ulus basin, located in the north of Turkey adjacent to the Black Sea. A new coding implementation according to the class environment created in object oriented C++ programming language is carried out in structuring and building the solver. The model is based on the Godunov type finite volume scheme on unstructured triangular meshes. A mass balance preserving wet/dry boundary solution algorithm is integrated in the numerical scheme to satisfy the positive-depth condition and minimize the numerical instability when treating the propagation of wave front in regions of dry bed. The balance between bed slope and flux terms is also preserved for still water conditions on irregular topography. The 2-D solver is verified by simulating selected dam break cases, where good agreement with measured data is achieved. For the simulation of flood flows in the Ulus basin, in general, the simulated outflow hydrograph is found to compare well with the recorded data. A selected inundation map that is extracted from the model results is also presented to show the water surface level in the Floodplain.
- Rights:
- http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public
1847. An optimality system for finite average Markov decision chains under risk-aversion
- Creator:
- Alanís-Durán, Alfredo and Cavazos-Cadena, Rolando
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- partition of the state space, nonconstant optimal average cost, discounted approximations to the risk-sensitive average cost criterion, and equality of superior and interior limit risk-averse average criteria
- Language:
- English
- Description:
- This work concerns controlled Markov chains with finite state space and compact action sets. The decision maker is risk-averse with constant risk-sensitivity, and the performance of a control policy is measured by the long-run average cost criterion. Under standard continuity-compactness conditions, it is shown that the (possibly non-constant) optimal value function is characterized by a system of optimality equations which allows to obtain an optimal stationary policy. Also, it is shown that the optimal superior and inferior limit average cost functions coincide.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1848. An optimized evolutionary conditional independence Bayesian Classifier induction process
- Creator:
- Hruschka Jr., Estevam R., dos Santos , Edimilson B., and de O. Galvao, Sebastian D. C.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Bayesian learning, genetic algorithms, data mining, and hybrid intelligent systems
- Language:
- English
- Description:
- Bayesian Networks (BNs) are graphical models which represent multivariate joint probability distributions which have been used successfully in several studies in many application areas. BN learning algorithms can be remarkably effective in many problems. The search space for a BN induction, however, has an exponential dimension. Therefore, finding the BN structure that better represents the dependencies among the variables is known to be a NP problem. This work proposes and discusses a hybrid Bayes/Genetic collaboration (VOGAC-MarkovPC) designed to induce Conditional Independence Bayesian Classifiers from data. The main contribution is the use of MarkovPC algorithm in order to reduce the computational complexity of a Genetic Algorithm (GA) designed to explore the Variable Orderings (VOs) in order to optimize the induced classifiers. Experiments performed in a number of datasets revealed that VOGAC-MarkovPC required less than 25% of the time demanded by VOGAC-PC on average. In addition, when concerning the classification accuracy, VOGAC-MarkovPC performed as well as VOGAC-PC did.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1849. An optimized snowmelt lysimeter system for monitoring melt rates and collecting samples for stable water isotope analysis
- Creator:
- Rücker, Andrea, Zappa, Massimiliano, Boss, Stefan, and von Freyberg, Jana
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- snowmelt lysimeter, snowmelt collection, snowmelt rate, and stable water isotopes
- Language:
- Slovak
- Description:
- The contribution of snow meltwater to catchment streamflow can be quantified through hydrograph separation analyses for which stable water isotopes (18O, 2H) are used as environmental tracers. For this, the spatial and temporal variability of the isotopic composition of meltwater needs to be captured by the sampling method. This study compares an optimized snowmelt lysimeter system and an unheated precipitation collector with focus on their ability to capture snowmelt rates and the isotopic composition of snowmelt. The snowmelt lysimeter system consists of three individual unenclosed lysimeters at ground level with a surface of 0.14 m2 each. The unheated precipitation collector consists of a 30 cm-long, extended funnel with its orifice at 2.3 m above ground. Daily snowmelt samples were collected with both systems during two snowfall-snowmelt periods in 2016. The snowmelt lysimeter system provided more accurate measurements of natural melt rates and allowed for capturing the small-scale variability of snowmelt process at the plot scale, such as lateral meltwater flow from the surrounding snowpack. Because of the restricted volume of the extended funnel, daily melt rates from the unheated precipitation collector were up to 43% smaller compared to the snowmelt lysimeter system. Overall, both snowmelt collection methods captured the general temporal evolution of the isotopic signature in snowmelt.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1850. An ordered structure of pseudo-BCI-algebras
- Creator:
- Chajda, Ivan and Länger, Helmut
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- pseudo-BCI-algebra, directoid, antitone mapping, and pseudo-BCI-structure
- Language:
- English
- Description:
- In Chajda's paper (2014), to an arbitrary BCI-algebra the author assigned an ordered structure with one binary operation which possesses certain antitone mappings. In the present paper, we show that a similar construction can be done also for pseudo-BCI-algebras, but the resulting structure should have two binary operations and a set of couples of antitone mappings which are in a certain sense mutually inverse. The motivation for this approach is the well-known fact that every commutative BCK-algebra is in fact a join-semilattice and we try to obtain a similar result also for the non-commutative case and for pseudo-BCI-algebras which generalize BCK-algebras, see e.g. Imai and Iséki (1966) and Iséki (1966).
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public