相关论文: Preconditioned Random Toeplitz Operators
In this paper, we study Hermitian quaternion Toeplitz matrices generated by quaternion-valued functions. We show that such generating function must be the sum of a real-valued function and an odd function with imaginary component. This…
We propose several circulant preconditioners for systems defined by some functions $g$ of Toeplitz matrices $A_n$. In this paper we are interested in solving $g(A_n)\mathbf{x}=\mathbf{b}$ by the preconditioned conjugate method or the…
In this thesis we study the preconditioning of square, non-symmetric and real Toeplitz systems. We prove theoretical results, which constitute sufficient conditions for the efficiency of the proposed preconditioners and the fast convergence…
Circulant preconditioners for functions of matrices have been recently of interest. In particular, several authors proposed the use of the optimal circulant preconditioners as well as the superoptimal circulant preconditioners in this…
Radial basis functions provide highly useful and flexible interpolants to multivariate functions. Further, they are beginning to be used in the numerical solution of partial differential equations. Unfortunately, their construction requires…
The conversion of resolvent conditions into semigroup estimates is crucial in the stability analysis of hyperbolic partial differential equations. For two families of multiple Toeplitz operators, we relate the power bound with a resolvent…
We extend the operator preconditioning framework [R. Hiptmair, Comput. Math. with Appl. 52 (2006), pp.~699--706] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their…
Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…
We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criteria for a…
In this paper, we analyze the spectra of the preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is employed to approximate the multi-dimensional…
We characterize bounded and compact positive Toeplitz operators defined on the Bergman spaces over the Siegel upper half-space.
When solving linear systems with nonsymmetric Toeplitz or multilevel Toeplitz matrices using Krylov subspace methods, the coefficient matrix may be symmetrized. The preconditioned MINRES method can then be applied to this symmetrized…
When a linear system Ax = y is solved by means of iterative methods (mainly CG and GMRES) and the convergence rate is slow, one may consider a preconditioner P. The use of such preconditioner changes the spectrum of the matrix defining the…
We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in $R^d$. As the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use an approach…
Preconditioning for multilevel Toeplitz systems has long been a focal point of research in numerical linear algebra. In this work, we develop a novel preconditioning method for a class of nonsymmetric multilevel Toeplitz systems, which…
In recent years, there has been a renewed interest in preconditioning for multilevel Toeplitz systems, a research field that has been extensively explored over the past several decades. This work introduces novel preconditioning strategies…
Shifted Laplacian multigrid preconditioner has become a tool du jour for solving highly indefinite Helmholtz equations. The idea is to add a complex damping to the original Helmholtz operator and then apply a multigrid processing to the…
Estimating the condition numbers of random structured matrices is a well known challenge, linked to the design of efficient randomized matrix algorithms. We deduce such estimates for Gaussian random Toeplitz and circulant matrices. The…
A block lower triangular Toeplitz system arising from time-space fractional diffusion equation is discussed. For efficient solutions of such the linear system, the preconditioned biconjugate gradient stabilized method and flexible general…
The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of…