By Hyeong In Choi, Rida T. Farouki, Chang Yong Han, Hwan Pyo Moon (auth.), Deepak Kapur (eds.)
This publication constitutes completely refereed post-conference court cases of the eighth Asian Symposium on computing device arithmetic, ASCM 2007, held in Singapore in December 2007.
The 22 revised complete papers and five revised poster papers offered including three invited lectures have been conscientiously chosen in the course of rounds of reviewing and development from sixty five submissions. The papers are equipped in topical sections on algorithms and implementations, numerical tools and functions, cryptology, and computational logic.
Read Online or Download Computer Mathematics: 8th Asian Symposium, ASCM 2007, Singapore, December 15-17, 2007. Revised and Invited Papers PDF
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Extra resources for Computer Mathematics: 8th Asian Symposium, ASCM 2007, Singapore, December 15-17, 2007. Revised and Invited Papers
190–196 (2007) 17. : Locating real multiple zeros of a real interval polynomial. In: Proc. 2006 International Symposium on Symbolic and Algebraic Computation (ISSAC 2006), pp. 310–317 (2006) 18. : On the location of zeros of an interval polynomial. , Zhi, L. ) Symbolic-Numeric Computation, pp. 167–184. Birkh¨ auser, Basel (2007) 19. : The nearest polynomial with a given zero, and similar problems. ACM SIGSAM Bulletin 33(4), 2–4 (1999) 20. : Nearest singular polynomials. J. Symbolic Computation 26(6), 667–675 (1998) 21.
Although  treats complex zeros, because of the above reason, we can use a similar method to the one in  to solve the problem in this paper. Furthermore, we extend the results of  as follows. First, we prove that a nearest polynomial exists when the number of perturbed coeﬃcients is more than one and I does not degenerate to a point. Second, we give a simpler explicit formula for the distance between f and a nearest polynomial f˜, together with a necessary and suﬃcient condition for the existence of f˜ when I consists of one point.
Note that this strongly simpliﬁes the certiﬁcation process of the algorithm designed in  since it is now reduced to compute the dimension of a Zariskiclosed algebraic set. This also allows us to use simpler matrices A (for which the aforementioned projections πi may be not proper) to avoid a growth of the coeﬃcients. 6]. Additionally, we prove that, There exists a Zariski-closed subset A Cn such that for all (a1 , . . , an ) ∈ Cn \ A, the ideal L ∂f ∂f ∂f − a1 , L − a2 , . . , L − an ∩ Q[X1 , .
Computer Mathematics: 8th Asian Symposium, ASCM 2007, Singapore, December 15-17, 2007. Revised and Invited Papers by Hyeong In Choi, Rida T. Farouki, Chang Yong Han, Hwan Pyo Moon (auth.), Deepak Kapur (eds.)