An abstract view of symmetric gaussian elimination is presented. Problems are viewed as an assembly of computational entities whose interdependence is modeled by a graph. An algorithmic transformation on the entities which can be associated with vertex removal, is assumed to exist. The elimination tree of the symmetric gaussian elimination figures the order in which these transformations are ap...

A new formulation for LU decomposition allows efficient representation of intermediate matrices while eliminating blocks of various sizes, i.e. during “undulantblock” elimination. Its efficiency arises from its design for block encapsulization, implicit in data structures that are convenient both for process scheduling and for memory management. Row/column permutations that can destroy such enc...

A new formulation for LU decomposition allows efficient representation of intermediate matrices while eliminating blocks of various sizes, i.e. during “undulantblock” elimination. Its efficiency arises from its design for block encapsulization, implicit in data structures that are convenient both for process scheduling and for memory management. Row/column permutations that can destroy such enc...

in this paper, we present a numerical algorithm for solving matrix equations $(a otimes b)x = f$  by extending the well-known gaussian elimination for $ax = b$. the proposed algorithm has a high computational efficiency. two numerical examples are provided to show the effectiveness of the proposed algorithm.

Predicting the running time of a parallel program is useful for determining the optimal values for the parameters of the implementation and the optimal mapping of data on processors. However, deriving an explicit formula for the running time of a certain parallel program is a difficult task. We present a new method for the analysis of parallel programs: simulating the execution of parallel prog...

Motivated by the need to formalize generation of fast running code for linear algebra applications, we show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category with biproducts. This shifts the traditional view of matrices as indexed structures to a type-level perspective analogous to that of the pointfree algebra of progr...

In this paper, we consider the problem of solving an 2 2 n n  sparse positive definite system b AU  , arising from the use of finite difference methods to solve an elliptic boundary value problem on an n n  mesh where 1 2   k n where k is a positive integer. The large sparse linear system can be solved directly in an efficient way using nested dissection method, originally proposed by Alan...

In this paper we show that the knowledge of noise statistics contaminating a signal can be effectively used to choose an optimal Gaussian filter to eliminate noise. Very specifically, we show that the additive white Gaussian noise (AWGN) contaminating a signal can be filtered best by using a Gaussian filter of specific characteristics. The design of the Gaussian filter bears relationship with t...