scholarly journals Finding the Zeros of a High-Degree Polynomial Sequence

2021 ◽  
Vol 29 (2) ◽  
pp. 119
Author(s):  
Vladimir L. Borsch ◽  
Peter I. Kogut
Keyword(s):  
Degree Polynomial ◽  
Polynomial Sequence ◽  
High Degree

scholarly journals Efficient high degree polynomial root finding using GPU

2017 ◽  
Vol 18 ◽  
pp. 46-56 ◽  
Author(s):  
Kahina Ghidouche ◽  
Abderrahmane Sider ◽  
Raphaël Couturier ◽  
Christophe Guyeux
Keyword(s):  
Degree Polynomial ◽  
Root Finding ◽  
High Degree ◽  
Polynomial Root Finding

Polynomial Surface Representation of Arbitrary Ship Forms

1960 ◽  
Vol 4 (02) ◽  
pp. 12-21 ◽  
Author(s):  
J. E. Kerwin
Keyword(s):  
Degree Polynomial ◽  
Surface Representation ◽  
Numerical Examples ◽  
Hydrodynamic Calculations ◽  
Analytic Expression ◽  
Hull Forms ◽  
High Degree ◽  
Polynomial Surface

This paper is concerned with the approximation of an arbitrary hull shape by an analytic expression to be used primarily for hydrodynamic calculations. A method is described which permits high-degree polynomial surface equations to be used as approximations of a wide variety of hull shapes. Numerical examples obtained with an IBM 704 computer show that the procedure produces hull forms which are sufficiently accurate for most hydrodynamic calculations.

scholarly journals Oblivious Sketching of High-Degree Polynomial Kernels

2020 ◽  
pp. 141-160 ◽  
Author(s):  
Thomas D. Ahle ◽  
Michael Kapralov ◽  
Jakob B. T. Knudsen ◽  
Rasmus Pagh ◽  
Ameya Velingker ◽  
...  
Keyword(s):  
Degree Polynomial ◽  
High Degree ◽  
Polynomial Kernels

scholarly journals New Possibilities and Applications of the Least Squares Collocation Method

2018 ◽  
Vol 173 ◽  
pp. 01012 ◽  
Author(s):  
Vasiliy Shapeev ◽  
Vasiliy Belyaev ◽  
Sergey Golushko ◽  
Semyon Idimeshev
Keyword(s):  
Least Squares ◽  
Numerical Method ◽  
Present Article ◽  
Collocation Method ◽  
Numerical Experiments ◽  
High Accuracy ◽  
Least Squares Collocation ◽  
Degree Polynomial ◽  
Anisotropic Plates ◽  
High Degree

Least squares collocation method (LSC) is a versatile numerical method for solving boundary value problems for PDE. The present article demonstrates the abilities of LSC to solve various problems – in particular, calculations of bending of isotropic irregular shaped plates and multi-layered anisotropic plates. In order to achieve higher accuracy, new versions of the method utilize high-degree polynomial spaces. The numerical experiments demonstrate high accuracy of the solutions.

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