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The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete [2] [3]: MP1 Some problems related to Job-shop scheduling; Knapsack problem, quadratic knapsack problem, and several variants [2] [3]: MP9 Some problems related to Multiprocessor scheduling
The method for general multiplication is a method to achieve multiplications with low space complexity, i.e. as few temporary results as possible to be kept in memory. . This is achieved by noting that the final digit is completely determined by multiplying the last digit of the multiplic
The predecessor of the Magma system was named Cayley (1982–1993), after Arthur Cayley.. Magma was officially released in August 1993 (version 1.0). Version 2.0 of Magma was released in June 1996 and subsequent versions of 2.X have been released approximately once per year.
Modified Richardson iteration is an iterative method for solving a system of linear equations.Richardson iteration was proposed by Lewis Fry Richardson in his work dated 1910.
It is NP-complete to solve Nurikabe, even when the involved numbers are 1 and 2 only. Further, consider these two rules of Nurikabe: Black cells form a connected area; Black cells cannot form 2 × 2 squares, Either one can be ignored, giving a total of three variants. As it turns out, they are all NP-complete. [2]
Microsoft Math 1.0: Part of Microsoft Student 2006 Microsoft Math 2.0 : Part of Microsoft Student 2007 Microsoft Math 3.0 : Standalone commercial product that requires product activation ; includes calculus support, digital ink recognition features and a special display mode for video projectors
This is a consequence of the fact that, because gcd(R, N) = 1, multiplication by R is an isomorphism on the additive group Z/NZ. For example, (7 + 15) mod 17 = 5, which in Montgomery form becomes (3 + 4) mod 17 = 7. Multiplication in Montgomery form, however, is seemingly more complicated.
To solve a linear system Ax = b with a preconditioner K = K 1 K 2 ≈ A, preconditioned BiCGSTAB starts with an initial guess x 0 and proceeds as follows: r 0 = b − Ax 0; Choose an arbitrary vector r̂ 0 such that (r̂ 0, r 0) ≠ 0, e.g., r̂ 0 = r 0; ρ 0 = (r̂ 0, r 0) p 0 = r 0; For i = 1, 2, 3, … y = K −1 2 K −1 1 p i−1; v = Ay ...
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