A new method for solving polynomial equations

Garside, Gerald R.; Jarratt, P.; Mack, C.

doi:10.1093/comjnl/11.1.87

Cited by 15 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Replacing B v _± in Q p by the order-preserving approximation involving T p _ 2 we generate a class of IF using simultaneous approximations to all the zeros. Using (17) and 14, (15), (16), etc., we obtain a class of IF, dependent explicitly on m v , v = 1, 2, ..., N, the first few members of which are given below:…”

Section: § 4 a Class Of Simultaneous Ifmentioning

confidence: 99%

An algorithm for the total, or partial, factorization of a polynomial

Farmer

Loizou

1977

Math. Proc. Camb. Phil. Soc.

View full text Add to dashboard Cite

A globally convergent algorithm is presented for the total, or partial, factorization of a polynomial. Firstly, a circle is found containing all the zeros. Secondly, a search procedure locates smaller circles, each containing a zero, and the multiplicities are then calculated. Thirdly, a simultaneous Iteration Function is used to accelerate convergence. The Iteration Function is chosen from a class of such functions derived herein to deal with the general case of multiple zeros; various properties of these functions are also discussed. Finally, sample numerical results are given which demon-strate the effectiveness of the algorithm.

show abstract

Section: § 4 a Class Of Simultaneous Ifmentioning

confidence: 99%

An algorithm for the total, or partial, factorization of a polynomial

Farmer

Loizou

1977

Math. Proc. Camb. Phil. Soc.

View full text Add to dashboard Cite

show abstract

“…To carry out the iterations we shall use (l) with 9k (z) given by (4) z~+l =zi + (k --t) u(k-~) u(k-1) = zl + 9~k where u =/'ft. …”

Section: E (Ks 03)mentioning

confidence: 99%

“…In Table 2 the approximation ~, with only correct figures, and the quantities as in Table I are reported for the 5-th-degree polynomial given by Dimsdale and cited in [4] : z 5 --3z' --(2 +i) z 3 + (t2 + 5 i) z*--(8 +8i) z +4i.…”

Section: Examplesmentioning

confidence: 99%

A class of iterative methods for holomorphic functions

Pomentale

1971

Numer. Math.

View full text Add to dashboard Cite

Two aspects of an iterative k-th-order procedure for solving equationsa) In the case where /(z) is a polynomial, the k-th-order method defines at each iteration a circle containing at least a zero of the polynomial. b) Each iteration function, when modified by introducing one parameter 2, has a descent property in the large, i.e. a$0>O can be found such that for 0 < 2 ~ 20: [1 (oJ~)[ < [/(z)], coa being the value of the iteration function at z and 2.

show abstract

Parametric and polariton scattering in noncentrosymmetric crystals

Polkovnikov

1992

J Russ Laser Res

View full text Add to dashboard Cite

A new method for solving polynomial equations

Cited by 15 publications

References 0 publications

An algorithm for the total, or partial, factorization of a polynomial

An algorithm for the total, or partial, factorization of a polynomial

A class of iterative methods for holomorphic functions

Parametric and polariton scattering in noncentrosymmetric crystals

Contact Info

Product

Resources

About