In this paper, we consider a generalization of Ebenbauer’s differential equation for non-symmetric matrix diagonalization to a flow on arbitrary complex semisimple Lie algebras. The flow is designed in such a way that the desired diagonalizations are precisely the equilibrium points in a given Cartan subalgebra. We characterize the set of all equilibria and establish a Morse-Bott type property ...

We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. In a second step, the frequencies and amplitudes of the decimated signal ...

Approaches to approximate diagonalization of variable-coefficient differential operators using similarity transformations are presented. These diagonalization techniques are inspired by the interpretation of the Uncertainty Principle by Fefferman, known as the SAK Principle, that suggests the location of eigenfunctions of self-adjoint differential operators in phase space. The similarity transf...

Signal processing techniques have been developed that use different strategies to bypass the Nyquist sampling theorem in order to recover more information than a traditional discrete Fourier transform. Here we examine three such methods: filter diagonalization, compressed sensing, and super-resolution. We apply them to a broad range of signal forms commonly found in science and engineering in o...

We construct an extension of diffusion geometry to multiple modalities through joint approximate diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, retrieval, and clustering demonstrating that the joint diffusio...

Linear Scaling DALTON (LSDALTON) is a powerful molecular electronic structure program that is the focus of software optimization projects in PRACE 1IP-WP7.2 and PRACE 1IP-WP7.5. This part of the project focuses on the introduction of parallel diagonalization routines from the ScaLAPACK library into the latest MPI version of LSDALTON. The parallelization work has involved three main tasks: i) Re...

In classical works, Hurewicz and Menger introduced two diagonalization properties for sequences of open covers. Hurewicz found a combinatorial characterization of these notions in terms of continuous images. Recently, Scheepers has shown that these notions are particular cases in a large family of diagonalization schemas. One of the members of this family is weaker than the Hurewicz property an...

A momentum-space approach of the density-matrix renormalization-group ~DMRG! method is developed. Ground-state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum Monte Carlo results. It is shown that the momentum-space DMRG is a very useful numerical tool for studying the Hubbard model and other fundamental models of interact...

We identify an integrable one-dimensional inhomogeneous three-site open spin chain which arises in the problem of diagonalization of twist-three quark-gluon evolution equations in QCD in the chiral-odd sector. Making use of the existence of a non-trivial 'hidden' integral of motion the problem of diagonalization of the evolution kernels is reduced to the study of a second order finite-differenc...