{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T04:17:42Z","timestamp":1742617062309,"version":"3.40.2"},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540111573"},{"type":"electronic","value":"9783540386216"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1981]]},"DOI":"10.1007\/3-540-11157-3_34","type":"book-chapter","created":{"date-parts":[[2012,2,25]],"date-time":"2012-02-25T17:37:08Z","timestamp":1330191428000},"page":"343-354","source":"Crossref","is-referenced-by-count":1,"title":["The algorithmic complexity of linear algebras"],"prefix":"10.1007","author":[{"given":"A.","family":"Alder","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"Strassen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,6,8]]},"reference":[{"key":"10_CR1","unstructured":"D. Bini, M. Capovani, G. Lotti and F. Romani 1979, O(n2.7799) complexity for matrix multiplication. Information Proc. Letters 8, pp. 234\u2013235."},{"key":"10_CR2","unstructured":"D. Bini 1979, Relations between EC-algorithms and APA-algorithms, applications. Nota interna B79\/8 (March 1979) I.E.I. Pisa."},{"key":"10_CR3","unstructured":"A. Borodin and I. Munro 1975, The Computational Complexity of Algebraic and Numeric Problems. American Elsevier."},{"key":"10_CR4","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/0024-3795(78)90012-5","volume":"19","author":"R.W. Brockett","year":"1978","unstructured":"R.W. Brockett and D. Dobkin 1978, On the optimal evaluation of a set of bilinear forms. Linear Algebra and its Applications 19, pp. 207\u2013235.","journal-title":"Linear Algebra and its Applications"},{"key":"10_CR5","unstructured":"D. Dobkin 1973, On the arithmetic complexity of a class of arithmetic computations. Thesis, Harvard University."},{"key":"10_CR6","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1145\/322003.322014","volume":"24","author":"C.M. Fiduccia","year":"1977","unstructured":"C.M. Fiduccia and I. Zalcstein 1977, Algebras having linear multiplicative complexity. Journal of the ACM 24, pp. 311\u2013331.","journal-title":"Journal of the ACM"},{"key":"10_CR7","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/0304-3975(78)90045-2","volume":"7","author":"H.F. Groote de","year":"1978","unstructured":"H.F. de Groote 1978, On varieties of optimal algorithms for the computation of bilinear mappings II. Optimal algorithms for 2\u00d72-matrix multiplication. Theoretical Computer Science 7, pp. 127\u2013148.","journal-title":"Theoretical Computer Science"},{"key":"10_CR8","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1137\/0120004","volume":"20","author":"J. Hopcroft","year":"1971","unstructured":"J. Hopcroft and L. Kerr 1971, On minimizing the number of multiplications necessary for matrix multiplication. SIAM J. Applied Math. 20. pp. 30\u201336.","journal-title":"SIAM J. Applied Math."},{"key":"10_CR9","unstructured":"T.D. Howell and J.C. Lafon 1975, The complexity of the quaternion product. Cornell University TR 75\u2013245."},{"key":"10_CR10","unstructured":"J.C. Lafon and S. Winograd 1980, to appear."},{"key":"10_CR11","first-page":"40","volume-title":"On two problems in abstract algebra connected with Horner's rule. Studies presented to R. von Mises","author":"A.M. Ostrowski","year":"1954","unstructured":"A.M. Ostrowski 1954, On two problems in abstract algebra connected with Horner's rule. Studies presented to R. von Mises, Academic Press, New York, pp. 40\u201348."},{"key":"10_CR12","unstructured":"V. Ya. Pan 1978, Strassen's algorithm is not optimal. Proc. 19th Ann. Symp. on Foundations of Computer Science, pp. 166\u2013176."},{"issue":"2","key":"10_CR13","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1137\/0209027","volume":"9","author":"V. Y. Pan","year":"1980","unstructured":"V. Ya. Pan 1980, New Fast Algorithms for Matrix Operations. SIAM J. on Computing, 9\/2, pp. 321\u2013342.","journal-title":"SIAM J. on Computing"},{"key":"10_CR14","doi-asserted-by":"crossref","unstructured":"V. Ya. Pan 1979, Field Extension and Trilinear Aggregating, Uniting and Cancelling for the Acceleration of Matrix Multiplication, Proc. 20th Ann. Symp. on Foundations of Computer Science, pp. 28\u201338.","DOI":"10.1109\/SFCS.1979.17"},{"key":"10_CR15","unstructured":"V.Ya. Pan 1980, New Combination of Methods for the Acceleration of Matrix Multiplication. Preprint, State University of New York at Albany."},{"key":"10_CR16","unstructured":"A. Sch\u00f6nhage 1979, Partial and Total Matrix Multiplication. TR, Mathematisches Institut der Universit\u00e4t T\u00fcbingen, June 1979."},{"key":"10_CR17","unstructured":"A. Sch\u00f6nhage 1980, Partial and Total Matrix Multiplication. TR, Math. Inst. Univ. T\u00fcbingen (January 1980). To appear."},{"key":"10_CR18","unstructured":"H.J. Stoss 1979, Private communication."},{"key":"10_CR19","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1007\/BF02165411","volume":"13","author":"V. Strassen","year":"1969","unstructured":"V. Strassen 1969, Gaussian Elimination is not Optimal. Numer. Math. 13, pp. 354\u2013356.","journal-title":"Numer. Math."},{"key":"10_CR20","first-page":"184","volume":"264","author":"V. Strassen","year":"1973","unstructured":"V. Strassen 1973, Vermeidung von Divisionen. J. f\u00fcr reine und angew. Mathematik 264, pp. 184\u2013202.","journal-title":"J. f\u00fcr reine und angew. Mathematik"},{"key":"10_CR21","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/0024-3795(71)90009-7","volume":"4","author":"S. Winograd","year":"1971","unstructured":"S. Winograd 1971, On multiplication of 2\u00d72 matrices. Linear Algebra Appl. 4, pp. 381\u2013388.","journal-title":"Linear Algebra Appl."},{"key":"10_CR22","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/BF01683270","volume":"10","author":"S. Winograd","year":"1977","unstructured":"S. Winograd 1977, Some bilinear forms whose multiplicative complexity depends on the field of constants. Math. Systems Theory 10, pp. 169\u2013180.","journal-title":"Math. Systems Theory"}],"container-title":["Lecture Notes in Computer Science","Algorithms in Modern Mathematics and Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-11157-3_34.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T20:14:42Z","timestamp":1742588082000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-11157-3_34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981]]},"ISBN":["9783540111573","9783540386216"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/3-540-11157-3_34","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1981]]}}}