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  2. Horner's method - Wikipedia

    en.wikipedia.org/wiki/Horner's_method

    This polynomial is further reduced to = + + which is shown in blue and yields a zero of −5. The final root of the original polynomial may be found by either using the final zero as an initial guess for Newton's method, or by reducing () and solving the linear equation. As can be seen, the expected roots of −8, −5, −3, 2, 3, and 7 were ...

  3. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. [8] For higher degrees, the specific names are not commonly used, although quartic polynomial (for degree four) and quintic polynomial (for degree five) are sometimes used. The names for the degrees may be applied to the ...

  4. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    Polynomial interpolation also forms the basis for algorithms in numerical quadrature (Simpson's rule) and numerical ordinary differential equations (multigrid methods). In computer graphics, polynomials can be used to approximate complicated plane curves given a few specified points, for example the shapes of letters in typography.

  5. Runge's phenomenon - Wikipedia

    en.wikipedia.org/wiki/Runge's_phenomenon

    The Weierstrass approximation theorem states that for every continuous function f(x) defined on an interval [a,b], there exists a set of polynomial functions P n (x) for n=0, 1, 2, ..., each of degree at most n, that approximates f(x) with uniform convergence over [a,b] as n tends to infinity, that is,

  6. Symmetric polynomial - Wikipedia

    en.wikipedia.org/wiki/Symmetric_polynomial

    The following polynomials in two variables X 1 and X 2 are symmetric: + + + + (+) as is the following polynomial in three variables X 1, X 2, X 3: . There are many ways to make specific symmetric polynomials in any number of variables (see the various types below).

  7. Splitting field - Wikipedia

    en.wikipedia.org/wiki/Splitting_field

    Finding roots of polynomials has been an important problem since the time of the ancient Greeks. Some polynomials, however, such as x 2 + 1 over R, the real numbers, have no roots. By constructing the splitting field for such a polynomial one can find the roots of the polynomial in the new field.

  8. Polynomial regression - Wikipedia

    en.wikipedia.org/wiki/Polynomial_regression

    A drawback of polynomial bases is that the basis functions are "non-local", meaning that the fitted value of y at a given value x = x 0 depends strongly on data values with x far from x 0. [9] In modern statistics, polynomial basis-functions are used along with new basis functions , such as splines , radial basis functions , and wavelets .

  9. Mathematics of paper folding - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_paper_folding

    In January 2002, she folded a 4,000-foot-long (1,200 m) piece of toilet paper twelve times in the same direction, debunking a long-standing myth that paper cannot be folded in half more than eight times. [21] [22] The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat, and making a single straight complete ...