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  2. Matrix multiplication algorithm - Wikipedia

    en.wikipedia.org/.../Matrix_multiplication_algorithm

    The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:

  3. Computational complexity of matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    The best known lower bound for matrix-multiplication complexity is Ω(n 2 log(n)), for bounded coefficient arithmetic circuits over the real or complex numbers, and is due to Ran Raz. [32] The exponent ω is defined to be a limit point, in that it is the infimum of the exponent over all matrix multiplication algorithms. It is known that this ...

  4. Computational complexity of mathematical operations - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, () below stands in for the complexity of the chosen multiplication algorithm.

  5. Basic Linear Algebra Subprograms - Wikipedia

    en.wikipedia.org/wiki/Basic_Linear_Algebra...

    HP's Math library supporting IA-64, PA-RISC, x86 and Opteron architecture under HP-UX and Linux. Intel MKL The Intel Math Kernel Library, supporting x86 32-bits and 64-bits, available free from Intel. [7] Includes optimizations for Intel Pentium, Core and Intel Xeon CPUs and Intel Xeon Phi; support for Linux, Windows and macOS. [37] MathKeisan

  6. Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Strassen_algorithm

    The left column visualizes the calculations necessary to determine the result of a 2x2 matrix multiplication. Naïve matrix multiplication requires one multiplication for each "1" of the left column. Each of the other columns (M1-M7) represents a single one of the 7 multiplications in the Strassen algorithm. The sum of the columns M1-M7 gives ...

  7. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    Computing the k th power of a matrix needs k – 1 times the time of a single matrix multiplication, if it is done with the trivial algorithm (repeated multiplication). As this may be very time consuming, one generally prefers using exponentiation by squaring , which requires less than 2 log 2 k matrix multiplications, and is therefore much ...

  8. Category:Matrix multiplication algorithms - Wikipedia

    en.wikipedia.org/wiki/Category:Matrix...

    See matrix multiplication algorithm. ... Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

  9. Hadamard product (matrices) - Wikipedia

    en.wikipedia.org/wiki/Hadamard_product_(matrices)

    The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.

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