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  2. Root-finding algorithm - Wikipedia

    en.wikipedia.org/wiki/Root-finding_algorithm

    Graeffe's method – Algorithm for finding polynomial roots; Lill's method – Graphical method for the real roots of a polynomial; MPSolve – Software for approximating the roots of a polynomial with arbitrarily high precision; Multiplicity (mathematics) – Number of times an object must be counted for making true a general formula

  3. Polynomial root-finding - Wikipedia

    en.wikipedia.org/wiki/Polynomial_root-finding

    The class of methods is based on converting the problem of finding polynomial roots to the problem of finding eigenvalues of the companion matrix of the polynomial, [1] in principle, can use any eigenvalue algorithm to find the roots of the polynomial. However, for efficiency reasons one prefers methods that employ the structure of the matrix ...

  4. Zero of a function - Wikipedia

    en.wikipedia.org/wiki/Zero_of_a_function

    A root of a polynomial is a zero of the corresponding polynomial function. [1] The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree , and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically ...

  5. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    An illustration of Newton's method. In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.

  6. Wilkinson's polynomial - Wikipedia

    en.wikipedia.org/wiki/Wilkinson's_polynomial

    Wilkinson's polynomial arose in the study of algorithms for finding the roots of a polynomial = =. It is a natural question in numerical analysis to ask whether the problem of finding the roots of p from the coefficients c i is well-conditioned. That is, we hope that a small change in the coefficients will lead to a small change in the roots.

  7. 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 ...

  8. Muller's method - Wikipedia

    en.wikipedia.org/wiki/Muller's_method

    Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) = 0.It was first presented by David E. Muller in 1956.. Muller's method proceeds according to a third-order recurrence relation similar to the second-order recurrence relation of the secant method.

  9. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    The zero polynomial is also unique in that it is the only polynomial in one indeterminate that has an infinite number of roots. The graph of the zero polynomial, f(x) = 0, is the x-axis. In the case of polynomials in more than one indeterminate, a polynomial is called homogeneous of degree n if all of its non-zero terms have degree n. The zero ...