Related papers: Krylov Distribution
The heat equation is often used in order to inpaint dropped data in inpainting-based lossy compression schemes. We propose an alternative way to numerically solve the heat equation by an extended Krylov subspace method. The method is very…
Energy distribution networks are crucial for human societies and since they often cover large geographical areas, their physical analysis is challenging. Modeling and simulation can be used to analyze such complex energy networks. In this…
We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a…
Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original $H$-theorem hypotheses do not fit here and the…
We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be…
The one-dimensional isotropic quantum Heisenberg spin systems with random couplings and random spin sizes are investigated using a real-space renormalization group scheme. It is demonstrated that these systems belong to a universality class…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem.…
Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…
We propose a tridiagonalization approach for non-Hermitian random matrices and Hamiltonians using singular value decomposition (SVD). This technique leverages the real and non-negative nature of singular values, bypassing the complex…
We characterize the Many-Body Localization (MBL) phase transition using the dynamics of spread complexity and inverse participation ratio in the Krylov space starting from different initial states. Our analysis of the disordered Heisenberg…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
We propose a two-dimensional (2d) quantum breakdown model of hardcore bosons interacting with disordered spins which would be classical without the bosons. It resembles particles incident into supersaturated vapor. The model exhibits a set…
In a scalar reaction-diffusion equation, it is known that the stability of a steady state can be determined from the Maslov index, a topological invariant that counts the state's critical points. In particular, this implies that pulse…
We consider the drift-diffusion equation $u_t-\epsilon\Delta u + \nabla \cdot(u\nabla K^*u)=0$ in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we restrict ourselves to the model case…
Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a…
This paper proves a Krylov-Safonov estimate for a multidimensional diffusion process whose diffusion coefficients are degenerate on the boundary. As applications the existence and uniqueness of invariant probability measures for the process…
Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. By…
LSQR, a Lanczos bidiagonalization based Krylov subspace iterative method, and its mathematically equivalent CGLS applied to normal equations system, are commonly used for large-scale discrete ill-posed problems. It is well known that LSQR…
A general inversion technique for the recovery of the underlying distribution function for observed galactic disks is presented and illustrated. Under the assumption that these disks are axi-symmetric and thin, the proposed method yields…