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  2. 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.

  3. 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 ...

  4. 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 ...

  5. 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 ...

  6. Numerical linear algebra - Wikipedia

    en.wikipedia.org/wiki/Numerical_linear_algebra

    For many problems in applied linear algebra, it is useful to adopt the perspective of a matrix as being a concatenation of column vectors. For example, when solving the linear system =, rather than understanding x as the product of with b, it is helpful to think of x as the vector of coefficients in the linear expansion of b in the basis formed by the columns of A.

  7. 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.

  8. 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 ...

  9. 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: