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  2. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form ⁠ + + ⁠ to the form ⁠ + ⁠ for some values of ⁠ ⁠ and ⁠ ⁠. [1] In terms of a new quantity ⁠ x − h {\displaystyle x-h} ⁠ , this expression is a quadratic polynomial with no linear term.

  3. Estimation of covariance matrices - Wikipedia

    en.wikipedia.org/wiki/Estimation_of_covariance...

    Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in R p × p ; however, measured using the intrinsic geometry of ...

  4. Multivariable calculus - Wikipedia

    en.wikipedia.org/wiki/Multivariable_calculus

    Multivariable calculus is used in many fields of natural and social science and engineering to model and study high-dimensional systems that exhibit deterministic behavior. In economics , for example, consumer choice over a variety of goods, and producer choice over various inputs to use and outputs to produce, are modeled with multivariate ...

  5. Covariance matrix - Wikipedia

    en.wikipedia.org/wiki/Covariance_matrix

    Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...

  6. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    A simplified version of the LLL factorization algorithm is as follows: calculate a complex (or p-adic) root α of the polynomial () to high precision, then use the Lenstra–Lenstra–Lovász lattice basis reduction algorithm to find an approximate linear relation between 1, α, α 2, α 3, . . . with integer coefficients, which might be an ...

  7. Multivariate statistics - Wikipedia

    en.wikipedia.org/wiki/Multivariate_statistics

    Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to ...

  8. Function of several real variables - Wikipedia

    en.wikipedia.org/wiki/Function_of_several_real...

    The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.

  9. Halley's method - Wikipedia

    en.wikipedia.org/wiki/Halley's_method

    In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name.