TY - CHAP A1 - Lickteig, Thomas A1 - Meer, Klaus A1 - Pardo, Luis Miguel T1 - Real Computation and Complexity, Dagstuhl seminar Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-4994 UR - http://drops.dagstuhl.de/opus/volltexte/2006/499/ PB - Internationale Begegnungs- und Forschungszentrum für Informatik CY - Dagstuhl ER - TY - GEN A1 - Meer, Klaus A1 - Lickteig, Thomas T1 - Semi-algebraic complexity - Additive complexity of matrix computational tasks T2 - Journal of Complexity N2 - This paper is devoted to the study of lower bounds on the inherent number of additions and subtractions necessary to solve some natural matrix computational tasks such as computing the nullspace, some band transformation, and some triangulation of a givenm×mmatrix. The additive complexities of such tasks are shown to grow asymptotically like that of them×mmatrix multiplication. The paper is a continuation of an earlier paper by the authors, and also of 4where multiplicative complexity has been considered. We also propose a formalization of semialgebraic computational tasks. Y1 - 1997 UR - http://www.sciencedirect.com/science/article/pii/S0885064X97904301 U6 - https://doi.org/10.1006/jcom.1997.0430 SN - 0885-064X VL - 13 IS - 1 SP - 83 EP - 107 ER - TY - GEN A1 - Meer, Klaus A1 - Lickteig, Thomas T1 - A note on testing the resultant T2 - Journal of Complexity N2 - Shub (in "From Topology to Computation: Proceedings of the Smalefest." (M. Hirsch, J. Marsden, and M. Shub, Eds.), pp. 281-301, Springer-Verlag, New York/Berlin, 1993) proposes to attack the complex PFull-size image (<1 K) versus the NPFull-size image (<1 K) problem by focussing on lower bounds on testing the resultant of quadratic forms for zero. Taking up this question we show in the present paper a lower bound of order n3 for the resultant. Y1 - 1995 UR - http://www.sciencedirect.com/science/article/pii/S0885064X85710163?np=y U6 - https://doi.org/10.1006/jcom.1995.1016 SN - 0885-064X VL - 11 IS - 3 SP - 344 EP - 351 ER -