Dauguma praktinių mokslinių, įvairių taikymų uždavinių yra spendžiami skaitiniais metodais. Šie metodai aktualūs ir mokymo aspektu. Įvairiose aukštosiose mokyklose studentai, studijuodami skaitinių metodų teoriją, sprendžia praktines užduotis, taigi tenka arba patiems programuodami algoritmus, arba naudoti kompiuterines programas. Šiame darbe nagrinėjami universalių kompiuterinių matematinių sistemų – MATLAB IR MATHCAD, kaip vieno svarbiausių skaitiniais metodais sprendžiamų uždavinių priemonės. Taip pat nagrinėjamas Excel programos panaudojimas netiesinių lygčių sprendimui skaitiniais metodais. Darbe išnagrinėti netiesinių lygčių sprendimo metodai, tokie kaip paprastųj����� iteracijų, pusiaukirtos, Niutono ir kirstinių metodai, jų realizacija kiekvienoje iš nurodytų programų. Pateikiant kiekvieną iš šių temų yra trumpai aprašyti patys metodai, lyginamos kiekvienos kompiuterinės programos galimybės spręsti uždavinius pagal šiuos metodus, jų funkcijų aprašymas, taikymai ir sprendimo pavyzdžiai. Darbe pristatyta sukurta kompiuterinė mokymo priemonė, skirta netiesinių lygčių sprendimo skaitiniais metodais įsisavinimui. / The most practical, scientific and various applied tasks are solved by using numerical methods. These methods are urgent in teaching aspect, too. The students of various higher schools are solving practical tasks when studying theory of numerical methods, therefore they have to programme algorithms by themselves or use computer programs. In this work there are analyzed universal computer algebra systems – Matlab and Mathcad – as the one of the most important measures of solving tasks by using numerical methods. Also there is analyzed the use of Excel program for the reason how to solve the nonlinear equation by using numerical methods. In the work there are analyzed methods of nonlinear equations solving, such as simple iterative, bisection, Newton and secant methods and their realization in each referred program.. There are described the very methods when presenting every those themes and comparised the possibilities of each computer program for the reason how to solve the tasks by using these methods. There is given description of methods functions, application and examples of solving. In the work there is presented created computer training appliance for the reason of mastering with nonlinear equation solving by using numerical methods.

Šiame darbe nagrinėjami netiesiniai daugdarų atpažinimo metodai ir daugiamačių duomenų projekcijos metodai. Siūloma jais spręsti keliais laisvės laipsniais besisukančio objekto orientacijos radimo problemą. Aprašomi MDS, Trianguliacijos, Sammon, RPM, mRPM, CCA, PCA, LLE, LE, HLLE, LTSA, SMACOF ir Isomap metodai. Su kai kuriais iš jų atliekami web-kamera gautų galvos atvaizdų tyrimai. Isomap algoritmo pagrindu sukuriama programinė įranga ir su ja taipogi atliekami galvos orientacijos tyrimai. / This paper deals with Analysis of non-linear manifold learning methods and multidimensional data projection methods. It is proposed use them in solving problem of detection of orientation of object, moving in few degrees of freedom. Methods described: MDS, triangulation, Sammon, RPM, mRPM, CCA, PCA, LLE, LE, HLLE, LTSA, SMACOF and Isomap. Some of them are used to analyze head images acquired by webcam.. Application is created which is then used to analyze head orientation by implementing Isomap method.

One of the main problems in neurosurgery is knowledge about human brain. It's very important to see the whole brain with its critical neurostructures in virtual reality. This document is about three dimensional human brain visualization strategies. Review most recently used three dimensional objects building strategies from two dimensional medical MRI images. This task was split into 4 significant problems: image segmentation, point-sets correspondence, image registration and its frequently used transformation functions with image matching measurements. All these problems were addressed reader to show most recently used algorithms with advantages and disadvantages. Atlas types, patterns and maps survey was introduced with widely popular brain model coordinate systems. In order to find a better correspondence between two point sets it was modeled a new robust and accurate Overhauser spline points location optimization algorithm. Instead of deletion outlier points from overloaded point set, this algorithm generates more points in other set at optimized points locations. Determination of an accurate point location and choosing the correct transformation function are the key steps in registration process. Whereas registration is vital task in precise human brain visualization for neurosurgeries at preoperative and intraoperative process.