Related papers: Nonlinear Accelerator Problems via Wavelets: 5. Ma…
We present the Complex Envelope Variable Approximation (CEVA) as the very useful and compact method for the analysis of the essentially nonlinear dynamical systems. It allows us to study both the stationary and non-stationary dynamics even…
We consider the solution of variational equations on manifolds by Newton's method. These problems can be expressed as root finding problems for mappings from infinite dimensional manifolds into dual vector bundles. We derive the…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
In this paper, we design constant modulus probing waveforms with good correlation properties for collocated multi-input multi-output (MIMO) radar systems. The main content is as follows: first, we formulate the design problem as a fourth…
For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate…
In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
We investigate wavelet-like localized solutions in nonlinear waveguides, enabled by complementary propagation constants embedded in domains of anomalous dispersion. They are carrier-envelope-phase stable and independent of fine details of…
We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…
Adaptive methods do not have a direct generalization to manifolds as the adaptive term is not invariant. Momentum methods on manifolds suffer from efficiency problems stemming from the curvature of the manifold. We introduce a framework to…
Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…