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  2. Polynomial regression - Wikipedia

    en.wikipedia.org/wiki/Polynomial_regression

    The above matrix equations explain the behavior of polynomial regression well. However, to physically implement polynomial regression for a set of xy point pairs, more detail is useful. The below matrix equations for polynomial coefficients are expanded from regression theory without derivation and easily implemented. [6] [7] [8]

  3. Group method of data handling - Wikipedia

    en.wikipedia.org/wiki/Group_method_of_data_handling

    Like linear regression, which fits a linear equation over data, GMDH fits arbitrarily high orders of polynomial equations over data. [6] [7] To choose between models, two or more subsets of a data sample are used, similar to the train-validation-test split.

  4. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    For example, given a = f(x) = a 0 x 0 + a 1 x 1 + ··· and b = g(x) = b 0 x 0 + b 1 x 1 + ···, the product ab is a specific value of W(x) = f(x)g(x). One may easily find points along W(x) at small values of x, and interpolation based on those points will yield the terms of W(x) and the specific product ab. As fomulated in Karatsuba ...

  5. Tschirnhaus transformation - Wikipedia

    en.wikipedia.org/wiki/Tschirnhaus_transformation

    In 1683, Ehrenfried Walther von Tschirnhaus published a method for rewriting a polynomial of degree > such that the and terms have zero coefficients. In his paper, Tschirnhaus referenced a method by René Descartes to reduce a quadratic polynomial ( n = 2 ) {\displaystyle (n=2)} such that the x {\displaystyle x} term has zero coefficient.

  6. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Given a quadratic polynomial of the form + + it is possible to factor out the coefficient a, and then complete the square for the resulting monic polynomial. Example: + + = [+ +] = [(+) +] = (+) + = (+) + This process of factoring out the coefficient a can further be simplified by only factorising it out of the first 2 terms.

  7. Linear least squares - Wikipedia

    en.wikipedia.org/wiki/Linear_least_squares

    Optimal instruments regression is an extension of classical IV regression to the situation where E[ε i | z i] = 0. Total least squares (TLS) [6] is an approach to least squares estimation of the linear regression model that treats the covariates and response variable in a more geometrically symmetric manner than OLS. It is one approach to ...

  8. Laguerre's method - Wikipedia

    en.wikipedia.org/wiki/Laguerre's_method

    In other words, Laguerre's method can be used to numerically solve the equation p(x) = 0 for a given polynomial p(x). One of the most useful properties of this method is that it is, from extensive empirical study, very close to being a "sure-fire" method, meaning that it is almost guaranteed to always converge to some root of the polynomial, no ...

  9. P-recursive equation - Wikipedia

    en.wikipedia.org/wiki/P-recursive_equation

    P-recursive equations are linear recurrence equations (or linear recurrence relations or linear difference equations) with polynomial coefficients. These equations play an important role in different areas of mathematics, specifically in combinatorics. The sequences which are solutions of these equations are called holonomic, P-recursive or D ...