Thời gian: 9h30 Thứ 5, 22/10/2015
Địa điểm: Phòng 201, Nhà A5, Viện Toán học, 18 Hoàng Quốc Việt, Cầu Giấy Hà Nội
Tóm tắt: On a computer, real numbers are usually represented by a finite set of numbers called floating-point numbers. When one performs an operation on these numbers, such as an evaluation by a function, one returns a floating-point number, close to the mathematical result of the operation. Ideally, this result should be the exact rounding of this mathematical value. One knows how to guarantee such a quality of results for arithmetical operations like +, -, x, / and square root but, as of today, it still remains a difficult issue when it comes to evaluate an elementary function such as cos, exp, cube root for instance. This problem, called Table Maker Dilemma, is actually a diophantine approximation problem, which has been tackled, in the last fifteen years, by V. Lefèvre, J.M. Muller, D. Stehlé, A. Tisserand and P. Zimmermann (LIP, ÉNS Lyon and LORIA, Nancy), using tools from algorithmic number theory. Their works made it possible to partially solve this question but it still remains an open problem. In this talk, I will present an ongoing joint work with Guillaume Hanrot (ÉNS Lyon, LIP, AriC), that improve the existing results.