Related papers: Balanced realizations of discrete-time stable all-…
Building black-box models for dynamical systems from data is a challenging problem in machine learning, especially when asymptotic stability guarantees are required. In this paper, we introduce a novel stability-ensuring and…
We consider continuous and discrete Schr\"odinger systems with self-adjoint matrix potentials and with additional dependence on time (i.e., dynamical Schr\"odinger systems). Transformed and explicit solutions are constructed using our…
We present quantum algorithms for simulating the dynamics of a broad class of classical oscillator systems containing $2^n$ coupled oscillators (Eg: $2^n$ masses coupled by springs), including those with time-dependent forces, time-varying…
We construct discrete time Markov chains that preserve the class of Schur processes on partitions and signatures. One application is a simple exact sampling algorithm for q^{volume}-distributed skew plane partitions with an arbitrary back…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…
Left-right and conjugation actions on matrix tuples have received considerable attention in theoretical computer science due to their connections with polynomial identity testing, group isomorphism, and tensor isomorphism. In this paper, we…
In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schr\"odinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position…
Use of the stochastic Galerkin finite element methods leads to large systems of linear equations obtained by the discretization of tensor product solution spaces along their spatial and stochastic dimensions. These systems are typically…
Developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering. A desirable feature to have in a numerical formulation for multiscale…
We propose a method for the spectral analysis of unbounded operator matrices in a general setting which fully abstains from standard perturbative arguments. Rather than requiring the matrix to act in a Hilbert space $\mathcal{H}$, we extend…
We present a hybridization technique for summation-by-parts finite difference methods with weak enforcement of interface and boundary conditions for second order, linear elliptic partial differential equations. The method is based on…
The operator-valued Schur-class is defined to be the set of holomorphic functions $S$ mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator…
We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norms of integral operators. As an illustration, we derive such…
This paper introduces the application of the asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, which asynchronous convergence is established under…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
In this paper, a linearized fully discrete scheme is proposed to solve the two-dimensional nonlinear time fractional Schr\"odinger equation with weakly singular solutions, which is constructed by using L1 scheme for Caputo fractional…
We propose a method to establish the rapid stabilization of the bilinear Schr\"odinger control system and its linearized system, and the finite time stabilization of the linearized system using the Grammian operators. The analysis of the…
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
The paper presents partial-realization theory and realization algorithms for linear switched systems. Linear switched systems are a particular subclass of hybrid systems. We formulate a notion of a partial realization and we present…