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  2. General algebraic modeling system - Wikipedia

    en.wikipedia.org/wiki/General_Algebraic_Modeling...

    The general algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maintainable models that can be ...

  3. Computational complexity of matrix multiplication - Wikipedia

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

    In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central subroutine in theoretical and numerical algorithms for numerical linear algebra and optimization, so finding the fastest algorithm for matrix multiplication is of major practical ...

  4. Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Strassen_algorithm

    This reduces the number of matrix additions and subtractions from 18 to 15. The number of matrix multiplications is still 7, and the asymptotic complexity is the same. [6] The algorithm was further optimised in 2017, [7] reducing the number of matrix additions per step to 12 while maintaining the number of matrix multiplications, and again in ...

  5. MATLAB - Wikipedia

    en.wikipedia.org/wiki/MATLAB

    MATLAB (an abbreviation of "MATrix LABoratory" [18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms , creation of user interfaces , and interfacing with programs written in other languages.

  6. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    Hadamard product of two matrices of the same size, resulting in a matrix of the same size, which is the product entry-by-entry; Kronecker product or tensor product, the generalization to any size of the preceding; Khatri-Rao product and Face-splitting product

  7. Matrix multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication...

    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:

  8. Matrix regularization - Wikipedia

    en.wikipedia.org/wiki/Matrix_regularization

    There are a number of matrix norms that act on the singular values of the matrix. Frequently used examples include the Schatten p-norms, with p = 1 or 2. For example, matrix regularization with a Schatten 1-norm, also called the nuclear norm, can be used to enforce sparsity in the spectrum of a matrix.

  9. Vectorization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Vectorization_(mathematics)

    B i consists of n block matrices of size m × m, stacked column-wise, and all these matrices are all-zero except for the i-th one, which is a m × m identity matrix I m. Then the vectorized version of X can be expressed as follows: vec ⁡ ( X ) = ∑ i = 1 n B i X e i {\displaystyle \operatorname {vec} (\mathbf {X} )=\sum _{i=1}^{n}\mathbf {B ...