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  2. Moore–Penrose inverse - Wikipedia

    en.wikipedia.org/wiki/Moore–Penrose_inverse

    The Octave programming language provides a pseudoinverse through the standard package function pinv and the pseudo_inverse() method. In Julia (programming language), the LinearAlgebra package of the standard library provides an implementation of the Moore–Penrose inverse pinv() implemented via singular-value decomposition. [25]

  3. Block matrix pseudoinverse - Wikipedia

    en.wikipedia.org/wiki/Block_matrix_pseudoinverse

    Instead of ([] []), we need to calculate directly or indirectly [citation needed] [original research? (), (), (), ().In a dense and small system, we can use singular value decomposition, QR decomposition, or Cholesky decomposition to replace the matrix inversions with numerical routines.

  4. Zero-forcing precoding - Wikipedia

    en.wikipedia.org/wiki/Zero-forcing_precoding

    When the channel state information is perfectly known at the transmitter, the zero-forcing precoder is given by the pseudo-inverse of the channel matrix. Zero-forcing has been used in LTE mobile networks. [2]

  5. Generalized inverse - Wikipedia

    en.wikipedia.org/wiki/Generalized_inverse

    In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of ...

  6. Constrained generalized inverse - Wikipedia

    en.wikipedia.org/.../Constrained_generalized_inverse

    So, a generalized inverse of () is also called a -constrained pseudoinverse of . An example of a pseudoinverse that can be used for the solution of a constrained problem is the Bott–Duffin inverse of constrained to , which is defined by the equation

  7. Woodbury matrix identity - Wikipedia

    en.wikipedia.org/wiki/Woodbury_matrix_identity

    A common case is finding the inverse of a low-rank update A + UCV of A (where U only has a few columns and V only a few rows), or finding an approximation of the inverse of the matrix A + B where the matrix B can be approximated by a low-rank matrix UCV, for example using the singular value decomposition.

  8. Invertible matrix - Wikipedia

    en.wikipedia.org/wiki/Invertible_matrix

    Although an explicit inverse is not necessary to estimate the vector of unknowns, it is the easiest way to estimate their accuracy and os found in the diagonal of a matrix inverse (the posterior covariance matrix of the vector of unknowns). However, faster algorithms to compute only the diagonal entries of a matrix inverse are known in many cases.

  9. Singular value decomposition - Wikipedia

    en.wikipedia.org/wiki/Singular_value_decomposition

    The SVD is also applied extensively to the study of linear inverse problems and is useful in the analysis of regularization methods such as that of Tikhonov. It is widely used in statistics, where it is related to principal component analysis and to correspondence analysis, and in signal processing and pattern recognition.