Modular Analysis of Almost Block Diagonal Systems of Equations

Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. It unveils a robust partial pivoting strategylocal pivoting. Extension of modular analysis to bordered systems is also included.