Related papers: Fast Symbolic Integer-Linear Spectra
We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil $(A,B)$. Based on Zolotarev's best rational function approximations of the signum function and conformal…
We give a specific method to solve with quadratic complexity the linear systems arising in known algorithms to deal with the sign determination problem. In particular, this enable us to improve the complexity bound for sign determination in…
Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…
A well-known fact in linear algebra is that $A^T A$ is always positive semi-definite for any real matrix $A$. We consider a generalization of this fact via the following decision problem. Given a symbolic product of length $k$, consisting…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…
This work introduces an approach to compute periodic phase diagram of micromagnetic systems by solving a periodic linearized Landau-Lifshitz-Gilbert (LLG) equation using an eigenvalue solver with the Finite Element Method formalism. The…
We review the enveloping algebra of the 10 dimensional chiral sigma matrices. To facilitate the computation of the product of several chiral sigma matrices we have developed a symbolic program. Using this program one can reduce the…
In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
We present an explicit polynomial formula for evaluating the principal logarithm of all matrices lying on the line segment $\{I(1-t)+At:t\in [0,1]\}$ joining the identity matrix $I$ (at $t=0$) to any real matrix $A$ (at $t=1$) having no…
A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized…
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…
The problem of the determination of the Hilbert-space metric which renders a given Hamiltonian $H$ self-adjoint is addressed from the point of view of applicability of computer-assisted algebraic manipulations. An exactly solvable example…
We extend the symbolic representation to the ring of N=1 supersymmetric differential polynomials, and demonstrate that operations on the ring, such as the super derivative, Frechet derivative and super commutator, can be carried out in the…
The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…
In this short note, we present a novel method for computing exact lower and upper bounds of eigenvalues of a symmetric tridiagonal interval matrix. Compared to the known methods, our approach is fast, simple to present and to implement, and…
We present a MATLAB package called the Pha-sorArray Toolbox that has been developed to make harmonic analysis and control methods both practical and user-friendly. The toolbox adopts an object-oriented architecture that enables intuitive…