The normal equations constructed by a Toeplitz matrix are studied, in order to nd a suitable preconditioner related to the discrete sine transform. New results are given about the structure of the product of two Toeplitz matrices, which allow the CGN method to achieve a superlinear rate of convergence. This preconditioner outperforms the circulant one for the iterative solution of Toeplitz leas...

Abstract. In the vicinity of extraordinary vertices, the action of a primal subdivision scheme for the construction of arbitrary topology surfaces can be represented by structured matrices that form a hybrid matrix algebra related to the block-circulant algebra. Exploiting the block diagonalization of such matrices, we can easily take into consideration the constraints to be satisfied by their ...

We consider applying the preconditioned conjugate gradient (PCG) method to solve linear systems Ax = b where the matrix A comes from the discretization of second-order elliptic operators. Let (L +)) ?1 (L t +) denote the block Cholesky factorization of A with lower block triangular matrix L and diagonal block matrix. We propose a preconditioner M = (^ L +)) ?1 (^ L t +) with block diagonal matr...

We prove that standard Gaussian random multipliers are expected to stabilize numerically both Gaussian elimination with no pivoting and block Gaussian elimination and that they also are expected to support the celebrated randomized algorithm for low-rank approximation of a matrix even without customary oversampling. Our tests show similar results where we apply random circulant and Toeplitz mul...

SUMMARY Strang's proposal to use a circulant preconditioner for linear systems of equations with a Hermitian positive definite Toeplitz matrix has given rise to considerable research on circulant preconditioners. This paper presents an {e iϕ }-circulant Strang-type preconditioner.

a typical iranian carbonate matrix block surrounded by an open fracture was modeled in order to understand the fracture-matrix interaction and realize how to model the interaction best. the modeling was carried out by using a fine-scaled eclipse model in the single porosity mode (the fractures were explicitly modeled). the model was extended to a stack of 6 matrix blocks to understand block-to-...

Third generation mobile radio systems will employ TD-CDMA in their TDD mode. To increase the capacity and performance of this system, the receiver will contain a joint detector. Joint detection is equivalent to solving a least squares problem, which represents a significant computational effort because of the amount of data that is involved. Therefore, algorithms and implementations must be dev...

This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the help of recent decoupling techniques and matrix-valued Bernstein inequalities, we obtain a new bound k = O(ǫ log(n)) for Gaussian circulant JL embeddings. Moreo...

Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matric...

In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three–dimensional boundary value problems governed by elliptic systems of partial differential equations. In particular, we consider problems arising in linear elasticity in axisymmetric domains. The proposed algorithm exploits the block circulant structure of the coeffic...