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  2. Mean of a function - Wikipedia

    en.wikipedia.org/wiki/Mean_of_a_function

    In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over the interval (a,b) is defined by: [1] ¯ = ().

  3. Algorithms for calculating variance - Wikipedia

    en.wikipedia.org/wiki/Algorithms_for_calculating...

    Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.

  4. Rosenbrock function - Wikipedia

    en.wikipedia.org/wiki/Rosenbrock_function

    Plot of the Rosenbrock function of two variables. Here a = 1 , b = 100 {\displaystyle a=1,b=100} , and the minimum value of zero is at ( 1 , 1 ) {\displaystyle (1,1)} . In mathematical optimization , the Rosenbrock function is a non- convex function , introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for ...

  5. Triangular distribution - Wikipedia

    en.wikipedia.org/wiki/Triangular_distribution

    This distribution for a = 0, b = 1 and c = 0.5—the mode (i.e., the peak) is exactly in the middle of the interval—corresponds to the distribution of the mean of two standard uniform variables, that is, the distribution of X = (X 1 + X 2) / 2, where X 1, X 2 are two independent random variables with standard uniform distribution in [0, 1]. [1]

  6. Minimum mean square error - Wikipedia

    en.wikipedia.org/wiki/Minimum_mean_square_error

    Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.

  7. 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.

  8. Contraharmonic mean - Wikipedia

    en.wikipedia.org/wiki/Contraharmonic_mean

    It is not monotonic − increasing a value of can decrease the value of the contraharmonic mean. For instance C(1, 4) > C(2, 4).. The contraharmonic mean is higher in value than the arithmetic mean and also higher than the root mean square: ⁡ ⁡ ⁡ ⁡ ⁡ ⁡ () where x is a list of values, H is the harmonic mean, G is geometric mean, L is the logarithmic mean, A is the arithmetic mean, R ...

  9. Taylor expansions for the moments of functions of random ...

    en.wikipedia.org/wiki/Taylor_expansions_for_the...

    The above is obtained using a second order approximation, following the method used in estimating the first moment. It will be a poor approximation in cases where f ( X ) {\displaystyle f(X)} is highly non-linear.