scholarly journals A polynomial solution for the potato-peeling problem

1986 ◽  
Vol 1 (2) ◽  
pp. 155-182 ◽  
Author(s):  
J. S. Chang ◽  
C. K. Yap
Keyword(s):  
Polynomial Solution ◽  
Potato Peeling

On the Seven Position Synthesis of a 5-SS Platform Linkage

1997 ◽  
Vol 123 (1) ◽  
pp. 74-79 ◽  
Author(s):  
Qizheng Liao ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Reference Point ◽  
Polynomial Solution ◽  
Degree Of Freedom ◽  
Prismatic Joint ◽  
Movement Characteristics ◽  
Position Synthesis ◽  
Freedom Movement

This paper builds on Innocenti’s polynomial solution for the 5-SS platform that generates a one-degree of freedom movement through seven specified spatial positions of a rigid body. We show that his 60×60 resultant can be reduced to one that is 10×10. We then actuate the linkage using a prismatic joint on the sixth leg and determine the trajectory of the reference point through the specified positions. The singularity submanifold of this associated 6-SS platform provides information about the movement characteristics of the 5-SS linkage.

scholarly journals Lucas Polynomial solution of Nonlinear Differential Equations with Variable Delay

2019 ◽  
pp. 1-12 ◽  
Author(s):  
Sevin Gümgüm ◽  
Nurcan Baykuş Savaşaneril ◽  
Ömür Kıvanç Kürkçü ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Polynomial Solution ◽  
Variable Delay

scholarly journals On the Effective Implementation and Capabilities of the Least-Squares Collocation Method for Solving Second-Order Elliptic Equations

2021 ◽  
pp. 210-228
Author(s):  
В.А. Беляев
Keyword(s):  
Least Squares ◽  
Local Coordinate System ◽  
Polynomial Solution ◽  
Computation Time ◽  
Least Squares Collocation ◽  
Effective Implementation ◽  
Curvilinear Interface ◽  
Diffusion Convection ◽  
Second Order Elliptic Equations ◽  
And Diffusion

Исследованы возможности численного метода коллокации и наименьших квадратов (КНК) на примерах кусочно-полиномиального решения задачи Дирихле для уравнений Пуассона и типа диффузии-конвекции с особенностями в виде больших градиентов и разрыва решения на границах раздела двух подобластей. Предложены и реализованы новые hp-варианты метода КНК, основанные на присоединении внутри области малых и/или вытянутых нерегулярных ячеек, отсекаемых криволинейной границей раздела от исходных прямоугольных ячеек сетки, к соседним самостоятельным ячейкам. Выписываются с учетом особенности условия согласования между собой кусков решения в ячейках, примыкающих с разных сторон к границе раздела. Проведено сравнение результатов, полученных методом КНК и другими высокоточными методами. Показаны преимущества и достоинства метода КНК. Для ускорения итерационного процесса применены современные алгоритмы и методы: предобуславливание; свойства локальной системы координат в методе КНК; ускорение, основанное на подпространствах Крылова; операция продолжения на многосеточном комплексе; распараллеливание. Исследовано влияние этих способов на количество итераций и время расчетов при аппроксимации полиномами различных степеней. The capabilities of the numerical least-squares collocation (LSC) method of the piecewise polynomial solution of the Dirichlet problem for the Poisson and diffusion-convection equations are investigated. Examples of problems with singularities such as large gradients and discontinuity of the solution at interfaces between two subdomains are considered. New hp-versions of the LSC method based on the merging of small and/or elongated irregular cells to neighboring independent cells inside the domain are proposed and implemented. They cut off by a curvilinear interface from the original rectangular grid cells. Taking into account the problem singularity the matching conditions between the pieces of the solution in cells adjacent from different sides to the interface are written out. The results obtained by the LSC method are compared with other high-accuracy methods. Advantages of the LSC method are shown. For acceleration of an iterative process modern algorithms and methods are applied: preconditioning, properties of the local coordinate system in the LSC method, Krylov subspaces; prolongation operation on a multigrid complex; parallelization. The influence of these methods on iteration numbers and computation time at approximation by polynomials of various degrees is investigated.

scholarly journals Computational Methods for Production-Based Asset Pricing Models with Recursive Utility

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Eric Mark Aldrich ◽  
Howard Kung
Keyword(s):  
Asset Pricing ◽  
Solution Method ◽  
Value Function ◽  
Polynomial Solution ◽  
Dsge Models ◽  
Recursive Utility ◽  
Solution Quality ◽  
Global Method ◽  
Asset Pricing Models ◽  
Solution Methods

Abstract We compare local and global polynomial solution methods for DSGE models with Epstein- Zin-Weil utility. We show that model implications for macroeconomic quantities are relatively invariant to choice of solution method but that a global method can yield substantial improvements for asset prices and welfare costs. The divergence in solution quality is highly dependent on parameters which affect value function sensitivity to TFP volatility, as well as the magnitude of TFP volatility itself. This problem is pronounced for calibrations at the extreme of those accepted in the asset pricing literature and disappears for more traditional macroeconomic parameterizations.

3 1/2 DOF Polynomial Solution of the Inferential H2/H∞ Control Problem With Application to Metal Rolling

1998 ◽  
Vol 120 (4) ◽  
pp. 445-455 ◽  
Author(s):  
M. J. Grimble
Keyword(s):  
Control Problem ◽  
Feedforward Control ◽  
Polynomial Solution ◽  
Degree Of Freedom ◽  
Force Measurements ◽  
Strip Rolling ◽  
Rolling Mills ◽  
Control Functions ◽  
Stochastic Optimal Control Problem ◽  
Feedback Tracking

The solution of a new inferential 3 1/2-degree-of-freedom stochastic optimal control problem is discussed which may be either H2 or H∞ optimal. The system includes a 2 1/2-degree-of-freedom inferential tracking controller and a feedforward control action. The feedback controller must be robust and is therefore normally designed to minimize an H∞, criterion. However, the solution obtained is sufficiently general that the feedback, tracking or feedforward control functions can be chosen to minimize either an H2 or a H∞ criterion. The inferential control problem considered was motivated by a problem in the control of metal strip rolling mills. The design study presented considers the control of strip thickness given stand force measurements, and the use of feedforward signal from an upstream stand.

scholarly journals On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 47 ◽  
Author(s):  
Mama Foupouagnigni ◽  
Salifou Mboutngam
Keyword(s):  
Difference Equation ◽  
Divided Difference ◽  
Polynomial Solution ◽  
Formal Proof ◽  
Second Order ◽  
Fixed Degree ◽  
Hypergeometric Type ◽  
The Mean ◽  
The Right

In this paper, we provide a formal proof of the existence of a polynomial solution of fixed degree for a second-order divided-difference equation of the hypergeometric type on non-uniform lattices, generalizing therefore previous work proving existence of the polynomial solution for second-order differential, difference or q-difference equation of hypergeometric type. This is achieved by studying the properties of the mean operator and the divided-difference operator as well as by defining explicitly, the right and the “left” inverse for the second operator. The method constructed to provide this formal proof is likely to play an important role in the characterization of orthogonal polynomials on non-uniform lattices and might also be used to provide hypergeometric representation (when it does exist) of the second solution—non polynomial solution—of a second-order divided-difference equation of hypergeometric type.

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