Let F(x) be a convex function defined in R^{n}), which is symmetric about the origin and homogeneous of degree 1, and let L be the lattice of integers Z^{n}. A definition of a reduced basis, b^{1},...,b^{n}, of the lattice with respect to the distance function F is presented, and we describe an...

The basic contracts traded on energy exchanges involve fixed-rate payments for the delivery of electricity over a certain period of time. It has been shown that options on these electricity swaps can be priced efficiently using a Hilbert space-valued time-inhomogeneous jump-diffusion model for...

In this work linear-quadratic optimal control problems for parabolic equations with mixed control-state constraints are considered. These problems arise when a Lavrentiev regularization is utilized for state constrained linear-quadratic optimal control problems. For the numerical solution a...

Proper orthogonal decomposition (POD) method has been successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, i.e., combine the classical finite volume element (FVE) method with the POD method to obtain a reduced-order FVE...

The construction of reduced-order models for parametrized partial differential systems using proper orthogonal decomposition (POD) is based on the information of the so-called snapshots. These provide the spatial distribution of the nonlinear system at discrete parameter and/or time instances....

This paper is devoted to a numerical solution technique for linear quadratic parabolic optimal control problems using the model order reduction technique of Proper Orthogonal Decomposition (POD). The proposed technique is an inexact gradient descent method where the step size is determined with...

Particle Image Velocimetry from the centerline of a 3 × 5 scaled down array of wind turbines in a wind tunnel was analyzed to gain further understanding of how turbulent transport brings mean kinetic energy (MKE) into the array from the neutrally stable Atmospheric Boundary Layer (ABL) above....

Implied volatility is a key value in financial mathematics. We discuss some of the pros and cons of the standard ways to compute this quantity, i.e. numerical inversion of the well-known Black–Scholes formula or asymptotic expansion approximations, and propose a new way to directly calculate...

The dynamics of coherent structures present in real-world environmental data is analyzed. The method developed in this paper combines the power of the Proper Orthogonal Decomposition (POD) technique to identify these coherent structures in experimental data sets, and its optimality in providing...