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Topic: Volker Strassen

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	Strassen algorithm - Wikipedia, the free encyclopedia
		In the mathematical discipline of linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm used for matrix multiplication.
		Volker Strassen published the Strassen algorithm in 1969.
		Strassen, Volker, Gaussian Elimination is not Optimal, Numer.
	en.wikipedia.org /wiki/Strassen_algorithm (405 words)

	CS 730 -- Assignment 1
		In 1969, Volker Strassen discovered an algorithm to multiply two n X n matrices in time O(n^(2.81)) instead of O(n^3) as is required by the standard algorithm.
		The cross over point observed in the previous question convinced many people that Strassen's algorithm (Winograd's variant) was impractical; however, if a hybrid algorithm is used, where the regular algorithm is used when it is faster than applying Strassen's algorithm, then the cross over point is much smaller.
		At each recursive step of Strassen's algorithm, if n is odd add an extra row and column of zeros so that A and B are embedded in (n+1) X (n+1) matrices A' and B'.
	www.mcs.drexel.edu /~jjohnson/2004-05/summer/cs680/assignments/assign1.html (619 words)

	CS 730 -- Assignment 1
		Shortly after Strassen's result, S. Winograd found a way to multiply 2 X 2 matrices using 7 multiplications and 15 additions/subtractions.
		Use Maple to verify that Winograd's variant of Strassen's algorithm is correct.
		The cross over point observed in part 2 convinced many people that Strassen's algorithm was impractical; however, if a hybrid algorithm is used, where the regular algorithm is used when it is faster than applying Strassen's algorithm, then the cross over point is much smaller.
	www.mcs.drexel.edu /~jjohnson/sp03/cs300/assignments/assign1.html (913 words)

	Algebra Glossary
		Strassen's algorithm for matrix multiplication is a method which can produce a matrix product more efficiently than the standard approach.
		It turns out that the number of quantities we have to define drops precipitously, and so the fact that we have to use a lot of extra additions to define them doesn't matter.
		But, as we have shown above, there are now implementations of the Strassen algorithm that beat the best implementations of the standard algorithm on the Cray.
	algebra-glossary.org.ru /q-t.htm (7749 words)

	Matthias Franz (Site not responding. Last check: 2007-10-26)
		Ph.D. thesis supervised by Volker Puppe, Universität Konstanz 2001
		diploma thesis supervised by Volker Strassen, Universität Konstanz 1997
		Together with Volker Puppe, I have organised the workshop "Calculations in Equivariant Cohomology" (Konstanz, 6-7 December 2002).
	www-fourier.ujf-grenoble.fr /~franz (207 words)

	ALGEBRAIC METHODS IN COMPUTATIONAL COMPLEXITY Home Page (Site not responding. Last check: 2007-10-26)
		Die Berechnungskomplexität von elementarsymmetrischen Funktionen und von Interpolationskoeffizienten, by Volker Strassen.
		The Complexity of Partial Derivatives, by Walter Baur and Volker Strassen.
		22.1: Schonhage's Proof of Strassen's lower bound for the symmetric polynomials.
	www.wisdom.weizmann.ac.il /~/shpilka/algebraic_methods (636 words)

	Oberwolfach Meeting on Complexity Theory (history)
		These meetings are organized on a voluntary basis by groups of researchers, pending on the approval of their proposal by the board of the Institute.
		The Meeting on Complexity Theory was initiated by Claus Schnorr and Volker Strassen, and took place for the first time in November 1974 (?, to be checked).
		The 10th meeting (organized by von zur Gathen, Schnorr, and Strassen), November 1992: report and personal impressions
	www.wisdom.weizmann.ac.il /~oded/pre-ober.html (269 words)

	[No title]
		An approach which avoids the use of ERH was found by Robert Solovay of IBM and Volker Strassen of the University of Zurich; theirs is a probabilistic algorithm which test primality of an m digit integer in O(m) steps.
		Solovay and Strassen noted that the set {a(a/n)=a(n-1)/2 mod n} is a proper subgroup of (ó/nó)* for composite n.
		This means that at least half the a's less than n and relatively prime to n do not satisfy (a/n)=a(n-1)/2 mod n.
	www.textfiles.com /law/primes.txt (2907 words)

	Citations: Gaussian elimination is not optimal - Strassen (ResearchIndex)
		Citations: Gaussian elimination is not optimal - Strassen (ResearchIndex)
		Strassen, "Gaussian Elimination is Not Optimal", Numerische Mathematick, 1969, Vol.
		Strassen, Gaussian Elimination is Not Optimal, Numerische Mathematik, vol.
	citeseer.ist.psu.edu /context/39985/0 (239 words)

	cs3323mid
		The details are too complicated to present on a test, but here is the overall idea.
		Let T(N) be the time complexity for Strassen's algorithm when multiplying
		Contrast the time complexities of the Strassen's algorithm and the usual algorithm.
	v5o5jotqkgfu3btr91t7w5fhzedjaoaz8igl.unbsj.ca /~owen/courses/3323-2001/cs3323mid (448 words)

	The Mathematics Genealogy Project - Volker Strassen
		Click here to see the students ordered by last name.
		According to our current on-line database, Volker Strassen has 9 students and 33 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	genealogy.math.ndsu.nodak.edu /html/id.phtml?id=36095&fChrono=1 (66 words)

	UC Berkeley Mathematics
		Professor Emeritus Robert M. Solovay has been named one of the winners of the 2003 Paris Kanellakis Theory and Practice Award by the Association for Computing Machinery.
		The other winners are Gary L. Miller, Carnegie Mellon University; Michael O. Rabin, Harvard University; and Volker Strassen, University of Konstanz.
		The winners were acknowledged ``for the development of efficient randomized tests of primality, enabling the practical realization of public key cryptography and demonstrating the power of randomized algorithms.''
	math.berkeley.edu /index.php?module=announce&ANN_user_op=view&ANN_id=26 (174 words)

	Harvard EECS: News and Events
		Professor of Computer Science, Michael Rabin, has received the Paris Kanellakis Award on behalf of the Association for Computing Machinery (ACM).
		He shares the honor with Gary Miller (Carnegie Mellon University), Robert Solovay (University of California at Berkeley), and Volker Strassen (University of Konstanz, Germany), "for the development of efficient randomized tests of primality, enabling the practical realization of public key cryptography and demonstrating the power of randomized algorithms."
		At the same ACM Award Banquet (June 5th in NYC) where Rabin will receive his award, Barbara Grosz, Radcliffe Institute Dean of Science and DEAS Computer Scientist, will be recognized as an ACM Fellow -- "distinguished colleagues to whom ACM and its members look for guidance and leadership as the world of information technology evolves."
	www.eecs.harvard.edu /index/eecs_news_events.php?p=15 (291 words)

	Professional Opportunities
		Based on Fermat's Little Theorem, that algorithm correctly identified composite numbers but had a small probability of error in identifying primes.
		Meanwhile, in 1977, Robert Solovay and Volker Strassen used quadratic residues to obtain another randomized polynomial-time algorithm that could be derandomized, assuming the Extended Riemann Hypothesis.
		In 1983, Leonard Adleman, Pomerance, and Robert Rumely came up with a deterministic algorithm that runs in something very close to polynomial time.
	www.siam.org /siamnews/09-02/primality.htm (1463 words)

	Gregory Bard's Research Homepage
		The work began with Volker Strassen's 1969 paper (which was only 3 pages by the way), showing a 2.81th power algorithm instead of the usual cubic algorithm.
		In reality, they are methods by which a tensor could be found, which would be a concise way of representing the algorithm with low theoretical complexity.
		Even a simple algorithm proposed by Schonhage, which beats Strassen's Algorithm, requires matrices of about 4 million rows and columns.
	www.math.umd.edu /~bardg (2068 words)

	[No title]
		Volker Strassen, Gaussian elimination is not optimal, Numerische Mathematik 13 (1969), 354--356
		Jon Louis Bentley and Michael Ian Shamos, Divide-and-conquer in multidimensional space, Proceedings of the 8th Annual ACM Symposium on Theory of Computing, ACM, New York (1976), 220--230
		Arnold Schönhage, Asymptotically fast algorithms for the numerical multiplication and division of polynomials with complex coefficients, Proceedings of the European Computer Algebra Conference, Lecture Notes in Computer Science 144, Springer-Verlag, Berlin/Heidelberg (1982), 3--15
	www.diku.dk /~jyrki/Course/Dat2P-1999/classics_in_algorithmics.html (507 words)

	Barry Mazur: ZoomInfo Business People Information (Site not responding. Last check: 2007-10-26)
		Barry Mazur's summary was automatically generated using 34 references found on the Internet.
		Michael F. Atiyah, Barry Mazur, John W&arg9=John W. Milnor>John W. Milnor, and Volker Strassen
		[9] Addresses on the Work of the 1986 Fields Medalists and Nevanlinna Prize Winner - Michael F. Atiyah, Barry Mazur, John W. Milnor, and Volker Strassen - AMS, 1987, 60 minutes, ISBN 0-8218-8006-3, List: US$51, VIDEO/7
	www.zoominfo.com /directory/Mazur_Barry_15891794.htm (500 words)

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