Much is already known about when a conjugate gradient method can be implemented with short recursions for the direction vectors. The work done in 1984 by Faber and Manteuuel 3] gave necessary and suucient conditions on the iteration matrix A, in order for a conjugate gradient method to be implemented with a single recursion of a certain form. However, this form does not take into account all po...

Recursion is a concept that can be used to describe the phenomena and natural occurrences in many different fields. As many applications utilize computer software to model recursion, recursion is a particularly important concept in the computing discipline. However, it is a difficult concept for many undergraduate students to master. A Recursion Graph (RGraph) is one visualization method for re...

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N , is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations with the the non-orthogonal localized basis set. This efficient inverting method can be incorporated in several O(N) methods for diagonalization of a gener...

In many cases, recursion removal improves the efficiency of recursive algorithms, especially algorithms with large formal parameters, such as All Pair Shortest path (APSP) algorithms. In this article, a recursion removal of the Seidel’s APSP [14] is presented, and a general method of recursion removal, called stack indexation is introduced.

As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to bemodified.Quantumdiagonalization involves unitary operatorswhose eigenvalues are different from one.

1 What makes a useful calculus? 7 1.0 The r^ ole of proofs and calculi in program development : 9 1.1 Choice of the proof 5 Conclusion 133 xii CONTENTS Chapter 0 Introduction Today there is general agreement that program development is important and diicult. Much research has been done and still is done, in order to make program development reliable and manageable. The main ingredients of progr...

In this article, we are concerned with the proofs of termination of rewrite systems by the method of interpretations. We propose a modiied approach to subrecursive hierarchies of functions by means of a syntactical approach to ordinal recursion. Our method appears to be appropriate for nding interpretations in a systematic way. We provide several examples of applications. It is shown that three...

We present the rst parallel, object-oriented C++ implementation of the dynamic recursion method. The recursion method is a means to tridiagonalize sparse matrices eeciently and is useful for a wide number of problems in physics. Dynamic recursion describes an optimization of the standard recursion method by operating only with a dynamically varying subset of basis vectors|reducing memory needs ...