Related papers: On the block Eberlein diagonalization method
The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: \ $-Mu+u^p=0$, where…
In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…
In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory…
We collect some results and notions concerning generalizations for block Jacobi matrices of several concepts, which have been important for spectral studies of the simpler and better known scalar Jacobi case. We focus here on some issues…
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…
We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…
Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues and eigenvectors of block tridiagonal matrices, which can be prohibitively expensive for large…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…
This work has introduced a generalized formulation of the problem of eigenvalue spectrum assignment for block matrix systems. In this problem, it is required to construct a feedback that provides that the matrix of the closed-loop system is…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…
This paper studies the $J$-method of [E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput. 36-4:A1978-A2001, 2014] for nonlinear eigenvector problems in a general Hilbert space framework. This is the basis for variational…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue problem becomes nonlinear. In the lossless case, linearization…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
A generalized eigenvector of a hypermatrix, called the universal (U-) eigenvector, is proposed, which extended the notion of diagonal (D-) eigenvectors in the literature. Using the semi-tensor product, the homogeneous U-eigenequation can be…
We prove a multiplier version of the Bernstein inequality on the complex sphere. Included in this is a new result relating a bivariate sum involving Jacobi polynomials and Gegenbauer polynomials, which relates the sum of reproducing kernels…
Diagonalizing a matrix $A$, that is finding two matrices $P$ and $D$ such that $A = PDP^{-1}$ with $D$ being a diagonal matrix needs two steps: first find the eigenvalues and then find the corresponding eigenvectors. We show that we do not…