An Efficient Method for Calculating Smoothing Splines Using Orthogonal Transformations.
An Eigenvalue Algorithm for Skew-Symmetric Matrices.
An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems
This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in Jones...
An explicit factorization of totally positive generalized Vandermonde matrices avoiding Schur functions.
An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation.
An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids
Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many...
An extension of the perturbation analysis for the Drazin inverse.
An imperfect conjugate gradient algorithm
A new biorthogonalization algorithm is defined which does not depend on the step-size used. The algorithm is suggested so as to minimize the total error after steps if imperfect steps are used. The majority of conjugate gradient algorithms are sensitive to the exactness of the line searches and this phenomenon may destroy the global efficiency of these algorithms.
An implicit approximate inverse preconditioner for saddle point problems.
An implicit restarted Lanczos method for large symmetric eigenvalue problems.
An improvement of Euclid's algorithm
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using - transformation and -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.
An incomplete-factorization preconditioning using repeated red-black ordering.
An intoduction to formal orthogonality and some of its applications.
This paper is an introduction to formal orthogonal polynomials and their application to Padé approximation, Krylov subspace methods for the solution of systems of linear equations, and convergence acceleration methods. Some more general formal orthogonal polynomials, and the concept of biorthogonality and its applications are also discussed.
An introduction to hierarchical matrices
An introduction to hierarchical matrices
We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short -matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrix-matrix...
An inverse eigenvalue problem for damped gyroscopic second-order systems.
An iterative algorithm for testing solvability of max-min interval systems
This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the algebraic structure in which classical addition and multiplication are replaced by and , where . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 and T5 solvability and give necessary and...
An Iterative Method for the Matrix Principal n-th Root
In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.
An iterative method of alternating type for systems with special block matrices
An iterative procedure for systems with matrices originalting from the domain decomposition technique is proposed. The procedure introduces one iteration parameter. The convergence and optimization of the method with respect to the parameter is investigated. The method is intended not as a preconditioner for the CG method but for the independent use.
An Iterative Substructuring Algorithm for Equilibrium Equations.