This volume of the Lecture Notes in Computer Science series contains the p- ceedings of the 3rd Conference on Numerical Analysis and Its Applications, which was held at the University of Rousse, Bulgaria, June 29-July 3, 2004. The conference was organized by the Department of Numerical Analysis and Statistics at the University of Rousse with the support of the Department of Mathematics of North Carolina State University. This conference continued the tradition of the two previous meetings (1996, 2000 in Rousse) as a forum where scientists from leading research groups from the "East" and "West" are provided with the opportunity to meet and exchange ideasandestablishresearchcooperations.Morethan100scientistsfrom28co- tries participated in the conference. A wide range of problems concerning recent achievements in numerical an- ysis and its applications in physics, chemistry, engineering, and economics were discussed. An extensive exchange of ideas between scientists who develop and studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lems took place during the conference. We thank the plenary lecturers, Profs. R. Lazarov and V. Thome, and the key lecturers and the organizers of the minisymposia, T. Boyadjiev, T. Donchev, E. Farkhi, M. Van Gijzen, S. Nicaise, and M. Todorov, for their contributions. We recognize the e?ort required to prepare these key lectures and organize the minisymposia. We appreciate your sharing your knowledge of modern hi- performancecomputingnumericalmethodswiththeconferenceparticipants.We also thank I. Brayanov for the help in putting together the book. The 4th Conference on Numerical Analysis and Its Applications will take place in 2008.