Abstract: First-order optimization algorithms, often preferred for large problems, require the gradient of the differentiable terms in the objective function. These gradients often involve linear ...

In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an ...

Abstract: We consider the problem of recovering the initial data (or initial state) of infinite-dimensional linear systems generated by a perturbed skew-adjoint operator. It is well-known that this ...

This work presents the mathematical/theoretical framework of the “nth-Order Feature Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint ...

ABSTRACT: When D is a linear partial differential operator of any order, a direct problem is to look for an operator D1 generating the compatibility conditions (CC) D1η = 0 of Dξ= η. Conversely, when ...

Let H be an infinite-dimensional separable complex Hilbert space and ${\cal B}(H)$ the algebra of all bounded linear operators on H. In this paper we characterize ...

This program attempts to provide a unique visualization of the root space of a semi-simple Lie algebra. Namely, the Special linear Lie algebra. This Lie algebra is the set of all nxn matrices over the ...

The Homogeneous System Solver is a computational program designed to solve matrix equations of the form Ax = 0. It automates matrix operations such as determinant calculation, cofactor extraction, ...