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An algebraic model of the subsystem for the computer generation of elimination operation

Ovsyak V., Ovsyak O., Kozelko M., Petrushka J.

Measurement Automation Monitoring

2018

Vol. 64, No. 3

48--52

A brief analysis of the known methods of non-algebraic and algebraic descriptions of algorithms has been presented. The features of the elimination operation being a term of the algorithm algebra have been shown. An algebraic model of the computer generation of the elimination operation has been synthesized by means of the algorithm algebra. The model has been implemented with the help of software on the platform Microsoft Visual Studio.NET. The models of subsystem as a graph and a diagram of sequences have been designed as well.

An Open Source GPU Accelerated Framework for Flexible Algebraic Reconstruction at Synchrotron Light Sources

Shkarin A., Ametova E., Chilingaryan S, Dritschler T., Kopmann A., Vogelgesang M., Shkarin R., Tsapko S.

Fundamenta Informaticae

2015

Vol. 141, nr 2/3

259--274

The recent developments in detector technology made possible 4D (3D + time) X-ray microtomographywith high spatial and time resolutions. The resolution and duration of such experiments is currently limited by destructive X-ray radiation. Algebraic reconstruction technique (ART) can incorporate a priori knowledge into a reconstruction model that will allow us to apply some approaches to reduce an imaging dose and keep a good enough reconstruction quality. However, these techniques are very computationally demanding. In this paper we present a framework for ART reconstruction based on OpenCL technology. Our approach treats an algebraic method as a composition of interacting blocks which performdifferent tasks, such as projection selection, minimization, projecting and regularization. These tasks are realised using multiple algorithms differing in performance, the quality of reconstruction, and the area of applicability. Our framework allows to freely combine algorithms to build the reconstruction chain. All algorithms are implemented with OpenCL and are able to run on a wide range of parallel hardware. As well the framework is easily scalable to clustered environment with MPI. We will describe the architecture of ART framework and evaluate the quality and performance on latest generation of GPU hardware from NVIDIA and AMD.

On bound for the solution of the unified algebraic Riccati equation

Czornik Adam

Matematyka Stosowana : matematyka dla społeczeństwa

1997

Nr 40

13--20

In recent years, several bounds of eigenvalues, norms and determinants for solutions of the continuous and discrete Riccati equations have been separately investigated. In this paper, an upper bound for the solution of the unified algebraic Riccati equations is presented. In the limit case, the result is reduced to a new upper bound for the solution of discrete and continuous Riccati equation.