MARC record from Internet Archive

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050 00 $aQA188$b.P36 1984
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100 1 $aPan, Victor.
245 10 $aHow to multiply matrices faster /$cVictor Pan.
260 $aBerlin ;$aNew York :$bSpringer-Verlag,$c1984.
300 $axi, 212 pages ;$c25 cm
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aLecture notes in computer science ;$v179
504 $aIncludes bibliographical references (pages 205-212) and index.
505 0 $apt. 1. The exponent of matrix multiplication. The power of recursive algorithms for matrix multiplication -- Bilinear algorithms for MM -- The search for a basis algorithm and the history of the asymptotic acceleration of MM -- the basic algorithm and the Exponent 2.67 -- The dependence of the exponent of MM on the class of constants used -- [Leaning T]-algorithms and their application to MM. Accumulation of the accelerating power of [leaning T]-algorithms via recursion -- Strassen's conjecture. Its extended and exponential versions -- Recursive algorithms for MM and for disjoint MM (definitions, notation, and two basic facts) -- Some applications of the recursive construction of bilinear algorithms -- Trilinear versions of bilinear algorithms and of bilinear [leaning T]-algorithms. Duality. Recursive trilinear algorithms -- Trilinear aggregating and some efficient basis designs -- A further example of trilinear aggregating and its refinement via a linear transformation of variables -- Aggregating the triplets of principal terms -- Recursive application of trilinear aggregating -- Can the exponent be further reduced? -- The exponents below 2.5 -- How much can we reduce the exponent? -- pt. 2. Correlation between matrix multiplication and other computational problems. Bit-time, bit-space, stability, and condition. -- Reduction of some combinatorial computational problems to MM -- Asymptotic arithmetical complexity of some computations in linear algebra -- Two block-matrix algorithms for the QR-factorization and QR-type factorization of a matrix -- Applications of the QR- and QR-type factorization to the problems MI, SLE, and Det -- Storage space for asymptotically fast matrix operations -- The bit-complexity of computations in linear algebra. The case of matrix multiplication -- Matrix norms and their application to estimating the bit-complexity of matrix multiplication -- Stability and condition of algebraic problems and of algorithms for such problems -- Estimating the errors of the QR-factorization of a matrix -- The bit-complexity and the condition of the problem of solving a system of linear equations -- The bit-complexity and the condition of the problem of matrix inversion -- The bit-complexity and the condition of the problem of the evaluation of the determinant of a matrix -- Summary of the bounds on the bit-time of computations in linear algebra; acceleration of solving a system of linear equations where high relative precision of the output is required -- pt. 3. The speed-up of the multiplication of matrices of a fixed size. The currently best upper bounds on the rank of the problem of MM of moderate sizes -- commutative quadratic algorithms for MM -- [Leaning T]-algorithms for the multiplication of matrices of small and moderate sizes -- The classes of straight line arithmetical algorithms and [leaning T]-algorithms and their reduction to quadratic ones -- The basic active substitution argument and lover bounds on the ranks of arithmetical algorithms for matrix multiplication -- Lower bounds on the [leaning T]-rank and on the commutative [leaning T]-rank of matrix multiplication -- Basic active substitution argument and lower bounds on the number of additions and subtractions -- Nonlinear lower bounds on the complexity of arithmetical problems under additional restrictions on the computational schemes -- A trade-off between the additive complexity and the asynchronicity of linear and bilinear algorithms -- An attempt of practical acceleration of matrix multiplication and of some other arithmetical computations.
650 0 $aMatrices$xData processing.
650 0 $aMultiplication$xData processing.
650 6 $aMatrices$xInformatique
650 6 $aMultiplication$xInformatique
650 7 $aMatrices$xData processing.$2fast$0(OCoLC)fst01012402
650 7 $aMultiplication$xData processing.$2fast$0(OCoLC)fst01029057
650 7 $aMatrices$xData processing.$2nli
650 7 $ainformatique$xmatrices (mathématiques)$xmultiplication.$2rero
655 4 $aElectronic resources (Books)
776 08 $iOnline version:$aPan, Victor.$tHow to multiply matrices faster.$dBerlin ; New York : Springer-Verlag, 1984$z3540138668$w(OCoLC)327018112
830 0 $aLecture notes in computer science ;$v179.
856 41 $3(n.149, 1983 - current) available via SpringerLink$uhttp://www.library.tufts.edu/ezproxy/ezproxy.asp?LOCATION=SpLinkLeNoCoSc
856 41 $3SpringerLink$uhttps://doi.org/10.1007/3-540-13866-8
856 41 $3Table of contents$uhttp://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2336581&custom_att_2=simple_viewer
856 41 $uhttp://link.springer.com/10.1007/3-540-13866-8$zSpringer Lecture Notes in Computer Science
856 41 $uhttp://link.springer.com/10.1007/3-540-13866-8
856 41 $uhttp://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=179$zRestricted to SpringerLink subscribers
856 4 $3Cover$uhttp://swbplus.bsz-bw.de/bsz009747222cov.htm$v20150917120338
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