The Strassen matrix multiplication can be categorized into divide-and-conquer algorithms, and they are known as the most efficient algorithms. We previously implemented them supporting multiple precision floating-point arithmetic using MPFR and Bailey's QD libraries and have shown their effectiveness in ...
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We have seen a lot of algorithms for matrix multiplication. Some are slow, like brute-force, in which we simply solve our problem with polynomial time. We also have fast algorithms using dynamic programming. Here we will use a memoization technique based on a divide and conquer approach. This...
An Error-Free Transformation for Matrix Multiplication with Reproducible Algorithms and Divide and Conquer Methods This paper discusses accurate numerical algorithms for matrix multiplication. Matrix multiplication is a basic and important problem in numerical linear algebra. Numerical computations using floating...
An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems Malyshev (1993), but improves on them in several ways. This algorithm only uses easily parallelizable linear algebra building blocks: matrix multiplication ... Z Bai,J Demmel,G Ming - 《Numerische Mathematik...
It is known that if this condition holds,\(A\)belongs to a set that forms a multiplicative group under ordinary matrix multiplication. Google Scholar Google Scholar Absil, P.-A., Mahony, R., Sepulchre, R., Van Dooren, P.: A Grassmann-Rayleigh quotient iteration for computing invariant sub...
P Godard,V Loechner,C Bastoul - Institute of Electrical and Electronics Engineers (IEEE) 被引量: 0发表: 2021年 Speeding up decimal multiplication We also present a simple cache-efficient algorithm for in-place $2n imes n$ or $n imes 2n$ matrix transposition, the need for which arises in...
In [1]: # Strassen's matrix multiplication algorithm.## Given two matrices A and B, start by padding them to be the same size, where# the number of rows and columns is a power of two. Then, it subdivides the# matrices into 2x2 block matrices, and uses a faster algorithm for multi...
methods where the matrix-vector multiplication is computed using a special fast method, such as the fast Fourier transform or the fast multipole method (... J Rahola - BIT 被引量: 112发表: 1996年 Separation of variables and the computation of Fourier transforms on finite groups, I This paper...
The task of the parallel job for the first parallel section is the multiplication of the shifted matrix by its transpose. The output of this task is a 22,277 × 22,277 matrix. However, such a matrix size cannot be allocated in the multicore platform. Therefore, in the multicore system,...