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  2. Condition number - Wikipedia

    en.wikipedia.org/wiki/Condition_number

    Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.

  3. Preconditioner - Wikipedia

    en.wikipedia.org/wiki/Preconditioner

    The better the approximation quality, the larger the matrix size is. In such a case, the goal of optimal preconditioning is, on the one side, to make the spectral condition number of to be bounded from above by a constant independent of the matrix size, which is called spectrally equivalent preconditioning by D'yakonov.

  4. Matrix Template Library - Wikipedia

    en.wikipedia.org/wiki/Matrix_Template_Library

    The Matrix Template Library (MTL) is a linear algebra library for C++ programs. The MTL uses template programming , which considerably reduces the code length. All matrices and vectors are available in all classical numerical formats: float , double , complex<float> or complex<double> .

  5. Array (data type) - Wikipedia

    en.wikipedia.org/wiki/Array_(data_type)

    The declaration var A: MyTable then defines a variable A of that type, which is an aggregate of eight elements, each being an integer variable identified by two indices. In the Pascal program, those elements are denoted A[1,1], A[1,2], A[2,1], …, A[4,2]. [3] Special array types are often defined by the language's standard libraries.

  6. Matrix representation - Wikipedia

    en.wikipedia.org/wiki/Matrix_representation

    Matrix representation is a method used by a computer language to store column-vector matrices of more than one dimension in memory. Fortran and C use different schemes for their native arrays. Fortran uses "Column Major" ( AoS ), in which all the elements for a given column are stored contiguously in memory.

  7. Row- and column-major order - Wikipedia

    en.wikipedia.org/wiki/Row-_and_column-major_order

    This was really only relevant for presentation, because matrix multiplication was stack-based and could still be interpreted as post-multiplication, but, worse, reality leaked through the C-based API because individual elements would be accessed as M[vector][coordinate] or, effectively, M[column][row], which unfortunately muddled the convention ...

  8. Conjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_gradient_method

    Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2). In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite.

  9. Singular value decomposition - Wikipedia

    en.wikipedia.org/wiki/Singular_value_decomposition

    where is the Givens rotation matrix with the angle chosen such that the given pair of off-diagonal elements become equal after the rotation, and where is the Jacobi transformation matrix that zeroes these off-diagonal elements. The iterations proceeds exactly as in the Jacobi eigenvalue algorithm: by cyclic sweeps over all off-diagonal elements.

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