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  2. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of ...

  3. Guyan reduction - Wikipedia

    en.wikipedia.org/wiki/Guyan_reduction

    The Guyan reduction is an integral part of the classic dynamic substructuring method known as the Craig-Bampton (CB) method. The static portion of the reduced system matrices derived from the CB method is a direct result of the Guyan reduction. It is calculated in the same manner as the Guyan stiffness matrix shown above.

  4. Wolff–Kishner reduction - Wikipedia

    en.wikipedia.org/wiki/Wolff–Kishner_reduction

    The Wolff–Kishner reduction is a reaction used in organic chemistry to convert carbonyl functionalities into methylene groups. [1][2] In the context of complex molecule synthesis, it is most frequently employed to remove a carbonyl group after it has served its synthetic purpose of activating an intermediate in a preceding step.

  5. Reductionism - Wikipedia

    en.wikipedia.org/wiki/Reductionism

    More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in computability (or recursive) theory, where it assumes the form of e.g. Turing reduction, but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it ...

  6. Integration by reduction formulae - Wikipedia

    en.wikipedia.org/wiki/Integration_by_reduction...

    e. In integral calculus, integration by reduction formulae is a method relying on recurrence relations. It is used when an expression containing an integer parameter, usually in the form of powers of elementary functions, or products of transcendental functions and polynomials of arbitrary degree, can't be integrated directly.

  7. Dimensionality reduction - Wikipedia

    en.wikipedia.org/wiki/Dimensionality_reduction

    Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many ...

  8. Carbonyl reduction - Wikipedia

    en.wikipedia.org/wiki/Carbonyl_reduction

    Carbonyl reduction. Oxidation ladders such as this one are used to illustrate sequences of carbonyls which can be interconverted through oxidations or reductions. In organic chemistry, carbonyl reduction is the conversion of any carbonyl group, usually to an alcohol. It is a common transformation that is practiced in many ways. [1]

  9. Low-rank approximation - Wikipedia

    en.wikipedia.org/wiki/Low-rank_approximation

    In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank.

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