Related papers: Fast Symbolic Integer-Linear Spectra
For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
Generative Adversarial Networks (GANs) are able to generate high-quality images, but it remains difficult to explicitly specify the semantics of synthesized images. In this work, we aim to better understand the semantic representation of…
The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorithm based on slicing the spectrum that takes advantage of the…
We present a prescription for forming matrices with specified eigenvalues and known eigenvectors. With this method, we can form Hermitian, anti-Hermitian, symmetric and general matrices with arbitrary eigenvalues. In addition we propose an…
Chandler-Wilde, Chonchaiya and Lindner conjectured that the set of eigenvalues of finite tridiagonal sign matrices ($\pm 1$ on the first sub- and superdiagonal, $0$ everywhere else) is dense in the set of spectra of periodic tridiagonal…
A wide class of matrix pencils connected with dissipative Hamiltonian descriptor systems is investigated. In particular, the following properties are shown: all eigenvalues are in the closed left half plane, the nonzero finite eigenvalues…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer…
Integrating symbolic knowledge and data-driven learning algorithms is a longstanding challenge in Artificial Intelligence. Despite the recognized importance of this task, a notable gap exists due to the discreteness of symbolic…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
A matrix $A$ is said to have $X$-simple image eigenspace if any eigenvector $x$ belonging to the interval $X=\{x\colon \underline{x}\leq x\leq\overline{x}\}$ is the unique solution of the system $A\otimes y=x$ in $X$. The main result of…
To understand the solution of a linear, time-invariant differential-algebraic equation, one must analyze a matrix pencil (A,E) with singular E. Even when this pencil is stable (all its finite eigenvalues fall in the left-half plane), the…
The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…
Evaluation of the eigenvectors of symmetric tridiagonal matrices is one of the most basic tasks in numerical linear algebra. It is a widely known fact that, in the case of well separated eigenvalues, the eigenvectors can be evaluated with…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
This paper introduces some efficient initials for a well-known algorithm (an inverse iteration) for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also…
We obtain simple formulas for the matrix elements of the resolvent operator (the Green's function) in any finite set of square integrable basis. These formulas are suitable for numerical computations whether the basis elements are…
It is common in machine learning and statistics to use symmetries derived from expert knowledge to simplify problems or improve performance, using methods like data augmentation or penalties. In this paper we consider the unsupervised and…