In many modern signal processing applications, in particular real-time
and adaptive signal processing, it turns out that there is a strong r
elationship between the algorithms (nested-loop type) that compute sol
utions to problems and the architectures (parallel/pipeline like) onto
which the algorithms can be or should be mapped. From this observatio
n it is believed that, within this class of applications, development
of algorithms and design of architectures could better be considered s
imultaneously. The framework in which such algorithms and architecture
s can best be expressed and designed is that of flow graphs which natu
rally describe both computations and communications between computatio
ns. In order to ensure a consistent design methodology, it is necessar
y to have a generic model and well-defined methods with which such des
igns can be formally undertaken. We introduce these ingredients in thi
s paper by analyzing the prototype application of linear equations sol
ving.