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We present a simple yet powerful framework for solving inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined near the true solution, and a numerical…
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…
The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the…
We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and implementations are provided for both small and large-scale…
The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example \cite{863046,863031} and the references therein). In this paper we develop a simple differential compensation (much…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
We study the electromagnetic fields of an arbitrarily moving charged particle and the radiation reaction on the charged particle using a novel approach. We first show that the fields of an arbitrarily moving charged particle in an inertial…
We developed a path integral formalism for the quantum mechanics in a rotating reference of frame, and proposed a spin path integral description for the spin degrees of freedom in it. We have also give some examples for the applications of…
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
A common task in single particle electron cryomicroscopy (cryo-EM) is the rigid alignment of images and/or volumes. In the context of images, a rigid alignment involves estimating the inner-product between one image of $N\times N$ pixels…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and…
A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…
This work presents a study on the nonrelativistic quantum motion of a charged particle in a rotating frame, considering the Aharonov-Bohm effect and a uniform magnetic field. We derive the equation of motion and the corresponding radial…
New integrable multi-atom matter-radiation models with and without rotating wave approximation (RWA) are constructed and exactly solved through algebraic Bethe ansatz. The models with RWA are generated through ancestor model approach in an…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…