Step-wise refinement is a powerful paradigm for developing a complex program from a simple program by adding features incrementally. We present the AHEAD (Algebraic Hierarchical Equations for Application Design) model that shows how step-wise refinement scales to synthesize multiple programs

ABSTRACT. We present an integral equation which generallzes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient

We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We

-gradient algorithms, indicating that I~QR is the most reliable algorithm when A is ill-conditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmation--least squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebra--linear systems (direct and

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Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite

to be developed in order to allow an efficient solution of even larger problems. This paper gives a review of the first hierarchical and purely matrix-based approach, algebraic multigrid (AMG). AMG can directly be applied, for instance, to efficiently solve various types of elliptic partial differential equations

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In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework

structures. Asymptotic methods based on complex analysis permit to extract directly coefficients of structurally complicated generating functions without a need for explicit coefficient expansions. Three major groups of problems relative to algebraic equations, differential equations, and iteration