Šiame magistro baigiamajame darbe yra nagrinėjami tiesinės algebros uždavinių sprendimai, panaudojant įvairias skaičiavimo priemones bei specializuotas bibliotekas. Pagrindinis darbo tikslas yra ištirti tokių uždavinių sprendimo būdus bei išnagrinėti jų išlygiagretinimo galimybes. Išanalizavus susijusią literatūrą, ištyrus pasirinktų tiesinių lygčių sistemų sprendimo algoritmus bei atlikus susijusius praktinius bandymus buvo pateikta detali algoritmų analizė bei jų panaudojimo rekomendacijos. Be to, panaudojant BalticGrid technologines galimybes, pavyko paskirstyti tiesinės algebros uždavinių sprendimą tarp keliasdešimties kompiuterių, tuo pačiu sumažinus bendrą užduočių skaičiavimo laiką. / The title of this work is “Parallel algorithms for linear algebra problems”. The main goal of Master thesis is to research solving possibilities of linear algebra problems, using different kind of computing machines and dedicated linear algebra libraries. In the beginning of the work author introduces the comparison of the system for parallel computing such as symmetric multi-processing and massively parallel processing. Later in this chapter the main linear algebra problems and theirs solutions were introduced. In the beginning of the second part, different kinds of algorithms for solving linear equation systems, such as LU factorization and SVD – singular value decomposition, were researched. In the next part of this chapter author looked for possibility to make computations of linear equation system in a parallel way. In the practical part of the work, the author developed few programs, which were used for analysis of different kind of algorithms and used BalticGrid technologies for parallel solving of linear equation systems. In the closing part of the work author presents the main results of the work and suggests some recommendations.

The problem of analyzing concurrent systems has been investigated by many researchers, and several solutions have been proposed. Among the proposed techniques, reachability analysis—systematic enumeration of reachable states in a finite-state model—is attractive because it is conceptually simple and relatively straightforward to automate and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. The system validation problem considered here is the problem of verifying that the original specification is itself logically consistent. If, for instance, the specification has a design error, an implementation is expected to pass a conformance test if it contains the same error. A validation for the logical consistency of the system, however, must reveal the design error. An automated analysis of all reachable states in a distributed system can be used to trace obscure logical errors that would be very hard to find manually. This type of validation is traditionally performed by the symbolic execution of a finite state machine model of the system studied. The author presents an overview of the existing validation techniques and methods. Specified and analyzed systems are presented as reachable state graph. The implementation of the aggregate specifications validation system is also presented.