Our method is based on the numerical evaluation of the integral which occurs in the Riemann Inversion formula. The trapezoidal rule approximation to this integral reduces to a Fourier series. We analyze the corresponding discretization error and demonstrate how this expression can be used in the development of an automatic routine , one in which the user needs to specify only the required accuracy.

Modern graphics processing units (GPUs) have been at the leading edge of increasing parallelism over the last 10 years. This fact has encouraged the use of GPUs in a broader range of applications, where developers are required to lever age this technology with new programming models which ease the task of writing programs to run efficiently on GPUs. In this paper, we discuss the main guidelines to assist the developer when porting sequential scientific code on modern GPUs. These guidelines were carried out by porting the L-BFGS, the (Limited memory-) BFGS algorithm for large scale optimization, available as Harwell routine VA15. The specific interest in the L-BFGS algorithm arises from the fact that this is the computational module with the longest running time of a Oceanographic Data Assimilation application software, on which some of the authors are working.