This note is a first attempt to perform waveform inversion by utilizing recent developments in semidefinite relaxations for polynomial equations to mitigate non-convexity. The approach consists in reformulating the inverse problem as a set of constraints on a low-rank moment matrix in a higher-dimensional space. While this idea has mostly been a theoretical curiosity so far, the novelty of this...

We consider eigenvalue problems for self-adjoint Sturm-Liouville difference equations of any even order. It is well known that such problems with Dirichlet boundary conditions can be transformed into an algebraic eigenvalue problem for a banded, real-symmetric matrix, and vice versa. In this article it is shown that such a transform exists for general separated, self-adjoint boundary conditions...

Symmetric spaces are well known in differential geometry from the study of spaces of constant curvature. The tangent space of a symmetric space forms a Lie triple system. Recently these objects have received attention in the numerical analysis community. A remarkable number of different algorithms can be understood and analyzed using the concepts of symmetric spaces and this theory unifies a ra...

Kaltofen has proposed a new approach in [8] for computing matrix determinants. The algorithm is based on a baby steps/giant steps construction of Krylov subspaces, and computes the determinant as the constant term of a characteristic polynomial. For matrices over an abstract field and by the results of Baur and Strassen [1], the determinant algorithm, actually a straight-line program, leads to ...

J = cost function N = number of impulses NLT = number of low-thrust-independent thrusters p = primer-vector magnitude p = primer vector pm = primer-vector absolute maximum r = relative position vector rj = space collocation of the jth impulse tf = final time tint = intermediate time tj = time instant of the jth impulse application tm = midcourse time corresponding to the primer absolute maximum...

Modern methods for H2-optimal model order reduction include the Iterative Rational Krylov Algorithm (IRKA, [Gugerkin, Antoulas, and Beattie, 2008]) and Parameterized Model Reduction (PMOR, [Baur, Beattie, Benner, and Gugercin, 2011]). In every IRKA or PMOR iteration, two sequences of shifted linear systems need to be solved, one for the shifted matrices and one for their adjoint, using the same...