We study the convergence of the iterations in a Hilbert space , where maps into itself and is a linear projection operator. The iterations converge to the unique fixed point of , if the operator is continuous and the Lipschitz constant . If an operator satisfies these assumptions and is an orthogonal projection such that , then the operator is defined and continuous in and satisfies .
We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S&P 500 Composite Index, the JP Morgan Government...
An explicit formula for the deflation of a tridiagonal matrix is presented. The resulting matrix is again tridiagonal.
For a two phase incompressible flow we consider a diffuse interface model aimed at addressing the movement of three-phase (fluid-fluid-solid) contact lines. The model consists of the Cahn Hilliard Navier Stokes system with a variant of the Navier slip boundary conditions. We show that this model possesses a natural energy law. For this system, a new numerical technique based on operator splitting and fractional time-stepping is proposed. The method is shown to be unconditionally stable. We present...