LIBRARIES

Design automation requires reliable methods for solving the equations describing the perfor-mance of the engineering system. While progress has been made to provide good algorithms for polynomial systems, we propose new techniques for the solution of general nonlinear al-gebraic systems. Moreover, the interval arithmetic approach we have chosen also guarantees numerical reliability. In this thesis we present a number of new algorithms that improve both the quality and the efficiency of existing interval arithmetic techniques for enclosing the solution of nonlin-ear algebraic equations. More specifically, we propose an exact algorithm for the solution of midpoint preconditioned linear interval equations. We extend existing techniques for au-tomatic compilation of fast partial derivatives to include interval slopes and have conceived a number of graph algorithms to improve their efficiency for general computational graphs. Furthermore, we have devised variable precision techniques to automatically control the required precision based on interval width. Finally, we have unified a number of enclosure languages using denotational semantics