Restructuring of Basic Linear Algebraic Algorithms

Abstract

Having obtained some useful information from the flow analysis options as described in section 3.1, and the vectorization of most of the DO loops of the central portion of the program has been accomplished, most of the work seems to have been done. Until now, though, we have not considered the algebraic structure of the basic algorithm. This is by far the most important consideration. Indeed, a good algorithm poorly coded is usually preferable to a poor one optimally coded |83|. For this reason, in the following chapters, we turn our attention to the restructuring of some basic linear algebraic algorithms such as matrix*vector and matrix*matrix, linear recursions up to more complex algorithms such as Gaussian elimination for full matrices, and iterative methods for the solution of linear algebraic systems of equations with sparse matrices (cf. |2|, |4|, |21|, |26|, |27|, |28|, |30|, |31|, |32|, |33|, |34|, |47|, |51|, |61|, |67|, |69|, |81|, |102|, |111|, |125|, |126|, |137|, |170|, |179|, |181|, |197|, |198| and |204| for sparse systems).