Gauss-Lobatto Formulae and Extremal Problems with Polynomials
نویسنده
چکیده
منابع مشابه
New results in extremal problems with polynomials
In this paper we give some new results in extremal problems with polynomials which are generalization of some results of F. Locher. 2000 Mathematical Subject Classification: 26D15, 65D32 In [6] F. Locher studies some extremal problems for semidefinition polynomials (nenegative or nepositive) with the dominant coefficient equal to 1. For this he uses the quadrature formulae with high algebraical...
متن کاملA novel modification of decouple scaled boundary finite element method in fracture mechanics problems
In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors (SIFs) play a crucial and significant role. Based on linear elastic fracture mechanics (LEFM), the SIFs and energy of cracked media may be estimated. This study presents the novel modification of decoupled scaled boundary finite element method (DSBFEM) to model cracked media. In this metho...
متن کاملA Gauss–Lobatto quadrature method for solving optimal control problems
This paper proposes a direct approach for solving optimal control problems. The time domain is divided into multiple subdomains, and a Lagrange interpolating polynomial using the Legendre–Gauss– Lobatto points is used to approximate the states and controls. The state equations are enforced at the Legendre–Gauss–Lobatto nodes in a nonlinear programming implementation by partial Gauss–Lobatto qua...
متن کاملOn Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae
Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the present note we show the positivity of the corresponding weights; this positivity has been conjectured already by Gautschi. As a consequence, we establish several ...
متن کاملGeneralized Gauss – Radau and Gauss – Lobatto Formulae ∗
Computational methods are developed for generating Gauss-type quadrature formulae having nodes of arbitrary multiplicity at one or both end points of the interval of integration. Positivity properties of the boundary weights are investigated numerically, and related conjectures are formulated. Applications are made to moment-preserving spline approximation. AMS subject classification: 65D30.
متن کامل