Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the development...

behavior of general root-finding algorithms is studied in numerical analysis. However, for polynomials specifically, the study of root-finding algorithms belongs...

computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is...

may provide all roots or all real roots; see Polynomial root-finding and Real-root isolation. Some polynomial, including all those of degree no greater than...

rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is...

Daniel Bernoulli, is a root-finding algorithm which calculates the root of largest absolute value of a univariate polynomial. The method works under...

In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials. In other words, Laguerre's method can be used to numerically...

distance between two roots. Such bounds are widely used for root-finding algorithms for polynomials, either for tuning them, or for computing their computational...

(see Root-finding algorithm). For polynomials with more than one indeterminate, the combinations of values for the variables for which the polynomial function...

equation (see Root-finding algorithm) and of the common solutions of several multivariate polynomial equations (see System of polynomial equations). The...

as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots...

The Jenkins–Traub algorithm for polynomial zeros is a fast globally convergent iterative polynomial root-finding method published in 1970 by Michael A...

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version...

Wilkinson's polynomial is a specific polynomial which was used by James H. Wilkinson in 1963 to illustrate a difficulty when finding the roots of a polynomial: the...

bisection method into efficient algorithms for finding all real roots of a polynomial; see Real-root isolation. The method is applicable for numerically...

of translation and motion of rotation. In 1729, he published a polynomial root-finding algorithm which became known as Bernoulli's method. His chief work...

difficulties of numerous computational problems, for example, polynomial root finding or computing eigenvalues. The condition number of f {\displaystyle...

gives only one root, even when both roots are positive. The Indian mathematician Brahmagupta included a generic method for finding one root of a quadratic...

autoregressive coefficients, whose zeros can be found analytically or with polynomial root finding algorithms. In contrast, MUSIC assumes that several such functions...

} Given any polynomial p, a root of p is a number y such that p(y) = 0. For example, the nth roots of x are the roots of the polynomial (in y) y n −...

interval, or finding a better functional approximation to f ( x ) {\displaystyle f(x)} . The latter usually means using a higher order polynomial in the approximation...

especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally...

exactly one root. This yields the oldest real-root isolation algorithm, and arbitrary-precision root-finding algorithm for univariate polynomials. For computing...

In this case, the factorization can be done with root-finding algorithms. The case of polynomials with integer coefficients is fundamental for computer...

Finding primitive roots modulo p is also equivalent to finding the roots of the (p − 1)st cyclotomic polynomial modulo p. The least primitive root gp...

non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since...

method for finding the cube root of numbers having many digits in the Aryabhatiya (section 2.5). Methods of computing square roots List of polynomial topics...

c to be a root of the polynomial x2 + x + c, an element of the splitting field of that polynomial. One verifies that R(c) + 1 is also a root. In terms...

square-free factorization reduces root-finding of a polynomial with multiple roots to root-finding of several square-free polynomials of lower degree. The square-free...

of P(x) is useful for finding the roots of P(x) itself. Hence the name “resolvent cubic”. The polynomial P(x) has a multiple root if and only if its resolvent...