Topic
Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: In this article, a unified method for solving algebracially quadratic, cubic and quartic equations is presented, which leads to a simple, complete system of the four solutions to the general quartic equation.
Abstract: It seems in the literature that methods for solving algebracially quadratic, cubic and quartic equations have very little in common. The goal of this article is to present a unified method for obtaining the algebraic solution of these equations. It is interesting to realize that the unified method presented here leads to a simple, complete system of the four solutions to the general quartic equation. The simplicity of this system of solutions makes it worthwhile to revisit some old problems related to cubic and quartic equations
12 citations
22 Jan 2020
TL;DR: In this article, the authors proposed a rational corrected scheme that results from convex combination between three local schemes, and the final interpolant has the form quintic numerator and quadratic denominator.
Abstract: This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R2). The higher R2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown’s validation.
12 citations
TL;DR: In this article, all quintic invariants in five variables with simple non-Abelian finite symmetry groups were constructed and defined by Calabi-Yau threefolds which are left invariant by the action of A5, A6, or PSL2(11).
Abstract: We construct all quintic invariants in five variables with simple non-Abelian finite symmetry groups These define Calabi–Yau threefolds which are left invariant by the action of A5, A6, or PSL2(11)
12 citations
TL;DR: A new method for function reconstruction from given integral values of successive subintervals by using quintic B-splines is studied, which is able to reconstruct the original function and its first-order to fourth-order derivatives.
Abstract: In this paper, we study a new method for function reconstruction from given integral values of successive subintervals by using quintic B-splines. The new method does not need any additional data and it is easy to implement. We are able to reconstruct the original function and its first-order to fourth-order derivatives. The reconstruction errors are well studied. Numerical results show that our method is very effective.
12 citations
TL;DR: In this paper, a bijection between binary quartic forms and quartic rings with a monogenic cubic resolvent ring was given, and a geometric interpretation of this parametrization was given.
Abstract: We give a bijection between binary quartic forms and quartic rings with a monogenic cubic resolvent ring, relating the rings associated to binary quartic forms with Bhargava's cubic resolvent rings. This gives a parametrization of quartic rings with monogenic cubic resolvents. We also give a geometric interpretation of this parametrization.
12 citations