Computation complexity of a broad variety of
practical design problems is known to be strongly
depending on an algebraic complexity of corresponding
mathematical system representations. Especially some
vector-matrix models are frequently used in numerous
interdisciplinary fields. One way to overcome the
complexity problems is based on some special algebraic
structures of low order model approximations, such as
e.g. balanced representations. Another approach based
on the concept of sparse matrices has also become very
popular. As a very successful special case of sparse
matrix based approach a class of tridiagonal system
representations [1] has found applications in solution of
partial differential equations, digital signal processing,
image processing, computational fluid dynamics, spline
curve fitting and many others. In this contribution a
generalized sparse matrix motivated multi-diagonal
method is proposed and some new results, based on state
space energy motivated causal system representations
are presented, too [2]
