the ecu convention on Numerical arithmetic and complicated functions (ENUMATH) is a sequence of meetings held each years to supply a discussion board for dialogue on fresh facets of numerical arithmetic and their purposes. The ?rst ENUMATH convention was once held in Paris (1995), and the sequence endured by means of the single in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This quantity incorporates a number of invited plenary lectures, papers provided in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10–14, 2007. we're chuffed that such a lot of humans have proven their curiosity during this convention. as well as the 10 invited shows and the general public lecture, we had greater than 240 talks in 9 minisymposia and ?fty 4 periods of contributed talks, and approximately 316 individuals from around the globe, especially from Europe. a complete of ninety eight contributions seem in those court cases. issues comprise theoretical facets of latest numerical thoughts and algorithms, in addition to to purposes in engineering and technological know-how. The booklet could be necessary for quite a lot of readers, giving them a good assessment of the main sleek equipment, innovations, algorithms and ends up in numerical arithmetic, scienti?c computing and their functions. we want to thank all of the members for the attendance and for his or her va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a wide contribution to the convention, the chair folks, and all speakers.