2 citations · 5 across the 14 of their papers we have counts for
14 papers
Convergence analysis of two-grid methods for symmetric positive semidefinite systems
Xuefeng Xu
Two-grid theory plays a fundamental role in the design and analysis of multigrid methods. This paper is devoted to a new convergence analysis of two-grid methods for singular and s…
Convergence analysis of two-grid methods for nonsymmetric positive definite systems
Xuefeng Xu
The convergence theory of multigrid methods for symmetric positive definite systems is well established. For nonsymmetric systems, however, the corresponding theory remains far fro…
Convergence analysis of two-level methods with general coarse solvers
Xuefeng Xu
Multilevel methods are among the most efficient numerical methods for solving large-scale linear systems that arise from discretized partial differential equations. The fundamental…
A new characterization of the convergence factor of two-level methods
Xuefeng Xu
Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level…
A new analytical framework for the convergence of inexact two-grid methods
Xuefeng Xu, Chen-Song Zhang
Two-grid methods with exact solution of the Galerkin coarse-grid system have been well studied by the multigrid community: an elegant identity has been established to characterize…
On the perturbation of the Moore-Penrose inverse of a matrix
Xuefeng Xu
The Moore-Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore-Penro…
On the perturbation of an -orthogonal projection
Xuefeng Xu
The -orthogonal projection onto a subspace is an important mathematical tool, which has been widely applied in many fields such as linear least squares problems, eigenvalue pr…
A new estimate for a quantity involving the Chebyshev polynomials of the first kind
Xuefeng Xu, Chen-Song Zhang
In this paper, we establish a new estimate (including lower and upper bounds) for an important quantity involved in the convergence analysis of smoothed aggregation algebraic multi…
On the Ideal Interpolation Operator in Algebraic Multigrid Methods
Xuefeng Xu, Chen-Song Zhang
Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-sui…
New upper bounds for the spectral variation of a general matrix
Xuefeng Xu
Let be a normal matrix with spectrum , and let be a perturbed matrix with spectrum $\…
A new expression for the Moore-Penrose inverse of a class of matrices
Xuefeng Xu
An expression for the Moore-Penrose inverse of a matrix of the form M = XNY , where X and Y are nonsingular, has been recently established by Castro-González et al. [1, Theorem 2.2…
New perturbation bounds for the spectrum of a normal matrix
Xuefeng Xu, Chen-Song Zhang
Let and be two normal matrices with spectra and , respect…
Generalization of the Sherman-Morrison-Woodbury formula involving the Schur complement
Xuefeng Xu
Let and be nonsingular matrices, and let . Explicit expressions for the Moore-Penrose inverses…
An improved upper bound for the number of distinct eigenvalues of a matrix after perturbation
Xuefeng Xu
An upper bound for the number of distinct eigenvalues of a perturbed matrix has been recently established by P. E. Farrell [1, Theorem 1.3]. The estimate is the central result in F…