Abstract

 
 
 The work is dedicated to the construction of numerical-analytical method of designing efficient algorithms for the solution of problems in economics and engineering. Using a priori information about the smoothness of the solution, great attention is paid to the construction of high-accuracy solutions. The proposed approach eliminates recurrent structure calculations unknown vectors decisions, which leads to the accumulation of rounding errors. Parallel form of the algorithm is the maximum, and therefore has the shortest possible time the implementation on parallel computing systems. Most conventional algorithms for solving these problems (sweep techniques, decomposition of the matrix into a product of two diagonal matrices, doubling, etc.) when multiple processors work typically no faster than if a single processor. The reason for this is substantial sequence computations of these algorithms.
 
 
Highlights
Problems that arise in front of the economists, are complex in their majority. This is because they depend on many factors, which influence each other, and determined time dependences [1]. This class of problems studied by means of economic and mathematical modeling [2, 3]
In this case we deal with the problems of mathematical modeling of this class of problems on parallel computing systems of cluster type
We propose to apply the net on value x with the step between nodes equal to
Summary
Problems that arise in front of the economists, are complex in their majority. This is because they depend on many factors, which influence each other, and determined time dependences [1]. An important feature of the solution given class of problems is their high computational complexity Their effective research tasks can be carried out only on the basis of multiprocessor systems [7, 8]. Existing methods for solving the problems of the economy and technology are not always suitable for reasons of accuracy, speed, memory requirements, the structure of algorithms, applicability for multi-processor computer systems In this context, there are new ideas and implemented in the field of computational mathematics. The purpose of this work is to construct the most parallel algorithms for solving the problems of the economy and technology, which are described by dynamic models In this case we deal with the problems of mathematical modeling of this class of problems on parallel computing systems of cluster type. After agreement (6) with equation (1) and equating the coefficients of equal powers we receive
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