Related papers: Bordering for spectrally arbitrary sign patterns

The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…

We consider an inverse spectral problem with the third-order differential equation and the non-separated boundary conditions. Two theorems on the uniqueness of the solution of this problem are proved, and a method for establishing the…

Motivated by a recent work on a preconditioned MINRES for flipped linear systems in imaging, in this note we extend the scope of that research for including more precise boundary conditions such as reflective and anti-reflective ones. We…

The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…

In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is…

We are interested in generating surfaces with arbitrary roughness and forming patterns on the surfaces. Two methods are applied to construct rough surfaces. In the first method, some superposition of wave functions with random frequencies…

Border complexity captures functions that can be approximated by low-complexity ones. Debordering is the task of proving an upper bound on some non-border complexity measure in terms of a border complexity measure, thus getting rid of…

Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the…

We achieve efficient shaping of superscattering by radially anisotropic nanowires relying on resonant multipolar interferences. It is shown that the radial anisotropy of refractive index can be employed to resonantly overlap electric and…

We propose an extended formalism for the spectral broadening function (BF) based on the multiplication rule of block matrices. The formalism, which we named the binary broadening function (BBF), can produce decomposed BFs for individual…

An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…

This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…

Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our…

This is the third article in a series of three dealing with the exploitation of speckle for imaging purposes. In complex media, a fundamental limit is the multiple scattering phenomenon that completely blurs the imaging process in depth.…

Even though image signals are typically acquired on a regular two dimensional grid, there exist many scenarios where non-regular sampling is possible. Non-regular sampling can remove aliasing. In terms of the non-regular sampling patterns,…

Any associative bilinear multiplication on the set of n-by-n matrices over some field of characteristic not two, that makes the same vectors orthogonal and has the same trace as ordinary matrix multiplication, must be ordinary matrix…

Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define…

We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors with symmetry (such as matrix multiplication and the…

We make an in-depth study of the known border rank (i.e. approximate) algorithms for the matrix multiplication tensor encoding the multiplication of an n x 2 matrix by a 2 x 2 matrix.

Speckle metrology exploits the high sensitivity of scattered fields to parameters of interest, yet this also leaves measurements vulnerable to unintended perturbations. Here we employ transmission matrix formalism to engineer light fields…