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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
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	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.