Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site utcsrgv.UUCP Path: utzoo!utcsrgv!phyllis From: phyllis@utcsrgv.UUCP (Phyllis Eve Bregman) Newsgroups: ont.events Subject: UofT DCS Seminar Schedule Message-ID: <1442@utcsrgv.UUCP> Date: Mon, 30-May-83 11:24:37 EDT Article-I.D.: utcsrgv.1442 Posted: Mon May 30 11:24:37 1983 Date-Received: Mon, 30-May-83 12:09:58 EDT Organization: CSRG, University of Toronto Lines: 25 UofT Department of Computer Science Seminar Schedule for the week of May 30th, 1983 Thursday, June 2nd, 2:00 P.M., SF1102: Professor Dario Bini, Dept. of Mathematics, University of Pisa, Italy: "Computational complexity, commutativity, and approximation". ABSTRACT: It is well-known that the computational complexity of a problem can be reduced either by allowing the commutative law or by using approximate algorithms. Introducing the concept of commutative rank and commutative border rank of a tensor, we state some lower bound criteria for the commutative and approximate complexity of evaluating sets of bilinear forms. We show that n/2(m+1) nonscalar multiplications are necessary and sufficient to approximate the of an mxn matrix and an n-vector, while mn are needed if either approximation or commutativity is disallowed. As a consequence, we show that the 2x2-matrix-vector product can be approximated by 6 nonscalar multiplications--while 7 are necessary without approximation--and that a value of a polynomial of degree n can be approximated using n/2 + 2 multiplications.