Hermite interpolation: The barycentric approach

The barycentric formulas for polynomial and rational Hermite interpolation are derived; an efficient algorithm for the computation of these interpolants is developed. Some new interpolation principles based on rational interpolation are discussed.

Some improvements of classical iterative methods for the solution of nonlinear equations

Penalty Function Methods for the Numerical Solution of Nonlinear Obstacle Problems with Finite Elements

A class of penalty function methods for the solution of nonlinear variational inequalities with obstacles ⩽ 0 fur alle v ⩾ ψ in the Sobolev space W1, p (ω) is studied. The (nonlinear) penalty equations are solved by finite element techniques; the order of convergence of this procedure which depends on the regularity of the solution as well as on the finite elements used is investigated. Eine Klasse von Penalty-Methoden zur Losung nichtlinearer Variationsungleichungen mit Hindernisnebenbedingungen ⩽ 0 fur alle v ⩾ ψ im Sobolev Raum W1, p (ω) wird untersucht. Die (nichtlinearen) Penalty-Gleichungen werden mit Hilfe der Finite Elemente Methode gelost; die Konvergenzordnung dieses Verfahrens, w…