enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Rational root theorem - Wikipedia

    en.wikipedia.org/wiki/Rational_root_theorem

    The theorem is used to find all rational roots of a polynomial, if any. It gives a finite number of possible fractions which can be checked to see if they are roots. If a rational root x = r is found, a linear polynomial ( x – r ) can be factored out of the polynomial using polynomial long division , resulting in a polynomial of lower degree ...

  3. Root-finding algorithm - Wikipedia

    en.wikipedia.org/wiki/Root-finding_algorithm

    In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f is a number x such that f ( x ) = 0 . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form , root-finding algorithms provide approximations to zeros.

  4. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    An important application is Newton–Raphson division, which can be used to quickly find the reciprocal of a number a, using only multiplication and subtraction, that is to say the number x such that ⁠ 1 / x ⁠ = a. We can rephrase that as finding the zero of f(x) = ⁠ 1 / x ⁠ − a. We have f ′ (x) = − ⁠ 1 / x 2 ⁠. Newton's ...

  5. Zeros and poles - Wikipedia

    en.wikipedia.org/wiki/Zeros_and_poles

    If f is a function that is meromorphic on the whole Riemann sphere, then it has a finite number of zeros and poles, and the sum of the orders of its poles equals the sum of the orders of its zeros. Every rational function is meromorphic on the whole Riemann sphere, and, in this case, the sum of orders of the zeros or of the poles is the maximum ...

  6. Geometrical properties of polynomial roots - Wikipedia

    en.wikipedia.org/wiki/Geometrical_properties_of...

    Root-finding of polynomials – Algorithms for finding zeros of polynomials; Square-free polynomial – Polynomial with no repeated root; Vieta's formulas – Relating coefficients and roots of a polynomial; Cohn's theorem relating the roots of a self-inversive polynomial with the roots of the reciprocal polynomial of its derivative.

  7. Jenkins–Traub algorithm - Wikipedia

    en.wikipedia.org/wiki/Jenkins–Traub_algorithm

    The Jenkins–Traub algorithm for polynomial zeros is a fast globally convergent iterative polynomial root-finding method published in 1970 by Michael A. Jenkins and Joseph F. Traub. They gave two variants, one for general polynomials with complex coefficients, commonly known as the "CPOLY" algorithm, and a more complicated variant for the ...

  8. Simple rational approximation - Wikipedia

    en.wikipedia.org/wiki/Simple_rational_approximation

    Simple rational approximation (SRA) is a subset of interpolating methods using rational functions. Especially, SRA interpolates a given function with a specific rational function whose poles and zeros are simple, which means that there is no multiplicity in poles and zeros. Sometimes, it only implies simple poles.

  9. Descartes' rule of signs - Wikipedia

    en.wikipedia.org/wiki/Descartes'_rule_of_signs

    To find the number of negative roots, change the signs of the coefficients of the terms with odd exponents, i.e., apply Descartes' rule of signs to the polynomial = + + This polynomial has two sign changes, as the sequence of signs is (−, +, +, −) , meaning that this second polynomial has two or zero positive roots; thus the original ...