Symbolic simplification and algebraic differentiation are only some of the advantages symbolic computations offer over their numerical counterparts. With a focus on sparse systems of linear equations, this contribution presents an analytical approach to a matrix inversion problem occurring in the field of Metabolic Flux Analysis. It is illustrated how the inherent complexity of the approach can...

In this paper, electromagnetic scattering problems are analyzed using an electric field integral equation (EFIE) formulation that is based on loop-star basis functions so as to avoid low-frequency instability problems. Moreover, to improve the convergence rate of iterative methods, a block matrix preconditioner (BMP) is applied to the EFIE formulation based on loop star-basis functions. Because...

In this paper, we study the relationship between the acquisition of time-harmonic seismic data and the Dirichlet-to-Neumann map for the Helmholtz equation in dimension n ≥ 3. This relationship is established through the introduction of a single-layer potential operator. We analyze its properties with a view to so-called iterative full waveform inversion based on the Hilbert-Schmidt norm, that i...

Most lattice Quantum Chromodynamics (QCD) formulations explicitly break chiral symmetry. This leads to unwanted mixing between operators of different chiral sectors, exceptional configurations when the simulated quark masses approach their physical values, and no clear definition of a topological index. The overlap Dirac operator solves these problems by satisfying a lattice variant of chiral s...

2] suggests that multiscale methods are a useful tool for purposes of computational efficiency. In this paper we explore a multiresolution approach We consider inverse problems described by that class to solving one dimensional inverse problems. The apof operators which are made sparse under the action proach we take is motivated by the work of Chou, of the wavelet transform [2]. Thus, the inve...

We consider the underdetermined blind source separation problem with linear instantaneous and convolutive mixtures when the input signals are sparse, or have been rendered sparse. In the underdetermined case the problem requires solving three subproblems: detecting the number of sources, estimating the mixing matrix, and finding an adequate inversion strategy to obtain the sources. This paper s...

Three-dimensional complete photonic-bandgap materials offer unique opportunities regarding the integration of optical waveguide architectures in three dimensions. However, corresponding experimental realizations are truly sparse. Here, we fabricate such waveguides using direct laser writing and a silicon double-inversion procedure. The optical characterization is in good agreement with theoreti...

We present an overview of our work on shape and spin state determination of asteroids from photometric data sparse in time. Our results are based on simulations that were performed using realistic shape and light-scattering models and time sequences that will be provided by Pan-STARRS (Panoramic Survey Telescope and Rapid Response System). We show some typical examples of physical model reconst...

Consider the solution of a large linear system when the coe cient matrix is sparse, symmetric, and positive de nite. One approach is the method of \conjugate gradient" (CG) with an incomplete Cholesky (IC) preconditioner (ICCG). A key problem with the design of a parallel ICCG solver is the bottleneck posed by repeated parallel sparse triangular solves to apply the preconditioner. Our work conc...

This article proposes novel sparsity-aware spacetime adaptive processing (SA-STAP) algorithms with l1-norm regularization for airborne phased-array radar applications. The proposed SA-STAP algorithms suppose that a number of samples of the full-rank STAP data cube are not meaningful for processing and the optimal full-rank STAP filter weight vector is sparse, or nearly sparse. The core idea of ...