Solving partial differential equations results in a continuum of regular and irregular stencil computation implementations. In this paper, we use heat diffusion on a bar to show how regular and irregular stencil computations are related, and then illustrate five complicating issues that occur in implementing the continuum of regular and irregular stencil computations in full applications. These...

in the process of structural analysis we often come to structures that can be analyzed with simpler methods than the standard approaches. for these structures, known as regular structures, the matrices involved are in canonical forms and their eigen-solution can be performed in a simple manner. however, by adding or removing some elements or nodes, such methods cannot be utilized. here, an effi...

This presentation is a generalization of 8] from square, regular n-by-n, pencils to singular and rectangular m-by-n pencils. We deene arithmetic-like operations on matrix pencils that are a natural extension of sums, products and quotients of real numbers. The algebra of linear transformations may be regarded as a special case of this pencil arithmetic. The language of linear relations leads to...