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strassen algorithm वाक्य

"strassen algorithm" हिंदी मेंstrassen algorithm in a sentence
उदाहरण वाक्यमोबाइल
  • They implemented numerous numerical algorithms including the Sch�nhage Strassen algorithm on this machine.
  • A more efficient multiplication algorithm is the Sch�nhage Strassen algorithm, which is based on the Fast Fourier transform.
  • The Strassen algorithm outperforms this " naive " algorithm; it needs only " n " 2.807 multiplications.
  • They in turn are applied in digital filters and as a rapid multiplication algorithm for polynomials and large integers ( Sch�nhage-Strassen algorithm ).
  • The number of additions and multiplications required in the Strassen algorithm can be calculated as follows : let be the number of operations for a matrix.
  • Modern algorithmic techniques based on the Sch�nhage Strassen algorithm for fast integer multiplication can be used to speed this up, leading to quasilinear algorithms for the GCD.
  • In linear algebra, the "'Strassen algorithm "', named after Volker Strassen, is an the fastest known algorithms for extremely large matrices.
  • Solving such a linear system is not practical due to extremely high time complexity of solving a linear system by the means of Gaussian Elimination or even Strassen algorithm.
  • An example is the Strassen algorithm for fast matrix multiplication, as well as the Hamming ( 7, 4 ) encoding for error detection and recovery in data transmissions.
  • In practice the Sch�nhage Strassen algorithm starts to outperform older methods such as Karatsuba and Toom Cook multiplication for numbers beyond 2 2 15 to 2 2 17 ( 10, 000 to 40, 000 decimal digits ).
  • Due to its overhead, Toom Cook is slower than long multiplication with small numbers, and it is therefore typically used for intermediate-size multiplications, before the asymptotically faster Sch�nhage Strassen algorithm ( with complexity ) becomes practical.
  • The Sch�nhage Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007, when a new method, F�rer's algorithm, was announced with lower asymptotic complexity; however, F�rer's algorithm currently only achieves an advantage for astronomically large values and is not used in practice.
  • As describes, the time for finding the fundamental solution using the continued fraction method, with the aid of the Sch�nhage Strassen algorithm for fast integer multiplication, is within a logarithmic factor of the solution size, the number of digits in the pair ( " x " 1, " y " 1 ).
  • Applications of the Sch�nhage Strassen algorithm include mathematical empiricism, such as the Great Internet Mersenne Prime Search and computing approximations of " ? ", as well as practical applications such as Kronecker substitution, in which multiplication of polynomials with integer coefficients can be efficiently reduced to large integer multiplication; this is used in practice by GMP-ECM for Lenstra elliptic curve factorization.
  • The predecessor to F�rer's algorithm, the Sch�nhage-Strassen algorithm, used Fast Fourier Transform ( FFT ) to compute integer products in time O ( n \ log n \ log \ log n ) ( in big O notation ) and its authors, Arnold Sch�nhage and Volker Strassen, also conjectured a lower bound for the problem of Here n denotes the total number of bits in the two input numbers.
  • For multiplication, the most straightforward algorithms used for multiplying numbers by hand ( as taught in primary school ) require O ( " N " 2 ) operations, but multiplication algorithms that achieve O ( " N " log ( " N " ) log ( log ( " N " ) ) ) complexity have been devised, such as the Sch�nhage Strassen algorithm, based on fast Fourier transforms, and there are also algorithms with slightly worse complexity but with sometimes superior real-world performance for smaller " N ".

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