2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
V. Shoup , Dept. of Comput. Sci., Toronto Univ., Ont., Canada
R. Smolensky , Dept. of Comput. Sci., Toronto Univ., Ont., Canada
It is shown that there is a set of points p/sub 1/, p/sub 2/,. . .,p/sub n/ such that any algebraic program of depth d for polynomial evaluation (or interpolation) at these points has size Omega (n log n/log d). Moreover, if d is a constant, then a lower bound of Omega (n/sup 1+1/d/) is obtained.
lower bound, polynomial evaluation, interpolation problems, algebraic program
V. Shoup, R. Smolensky, "Lower bounds for polynomial evaluation and interpolation problems", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 378-383, 1991, doi:10.1109/SFCS.1991.185394