A comparison of non-linear equation solvers
Dirk Nerinckx,Anny Haegemans +1 more
TLDR
The results and conclusions of the study of 10 FORTRAN and ALGOL programs for solving non-linear equations with one unknown, without using derivatives, are given.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1976-06-01 and is currently open access. It has received 23 citations till now. The article focuses on the topics: Fortran.read more
Citations
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Subdivision methods for solving polynomial equations
Bernard Mourrain,J. P. Pavone +1 more
TL;DR: A new algorithm for solving a system of polynomials, in a domain of R^n, which uses a powerful reduction strategy based on univariate root finder using Bernstein basis representation and Descarte's rule and gives new bounds for the complexity of approximating real roots in a box of R*n.
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Efficient Numerical Integration of the Equations of Motion of Non-Smooth Mechanical Systems
TL;DR: In this paper, a method for dealing with numerical integration of non-smooth mechanical dynamical systems is presented, based on the integration of piecewise smooth parts and piecing these parts together with appropriate transition conditions.
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An accurate Fortran code for computing hydrogenic continuum wave functions at a wide range of parameters
Liang-You Peng,Qihuang Gong +1 more
TL;DR: This work provides a code, which can generate accurate hydrogenic continuum wave functions and corresponding Coulomb phase shifts at a wide range of parameters and is able to give reliable results at the electron energy range and radial distances.
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A parallel algorithm for simple roots for polynomials
George H. Ellis,Layne T. Watson +1 more
TL;DR: Numerical results are presented which show the algorithm finds simple and multiple zeros to an accuracy (usually) limited by the accuracy of polynomial evaluation.
References
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An algorithm with guaranteed convergence for finding a zero of a function
TL;DR: An algorithm is presented for finding a zero of a function which changes sign in a given interval using linear interpolation and inverse quadratic interpolation with bisection and ALGOL 60 procedures.
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A modified regula falsi method for computing the root of an equation
M. Dowell,P. Jarratt +1 more
TL;DR: The Illinois method is briefly described and the asymptotic convergence of the method investigated in this paper, and numerical examples are also given including comparisons with other similar robust methods, including other robust methods.
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The “Pegasus” method for computing the root of an equation
TL;DR: In this article, a modified Regula Falsi method is described which is appropriate for use when an interval bracketing of the root is known, and the algorithm appears to exhibit superior asymptotic convergence properties to other modified linear methods.
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Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function
J. C. P. Bus,T. J. Dekker +1 more
TL;DR: Two algorithms are presented for finding a zero of a real continuous function defined on a given interval using mixtures of linear interpolation, rational interpolations, and bisectmn.