TY - JOUR

T1 - Parallelization of spline-wavelet decomposition

AU - Dem'yanovich, Yuri K.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A discrete spline-wavelet decomposition of the first order is discussed in the framework of the nonclassical approach. The purpose of this paper is to estimate the calculation duration for the discrete spline-wavelet decomposition with the use of two sorts of computers: One-Processor System (OPS) and Parallel Multi-processor System (PMS). The main object is the grid functions, which are named flows. The finite dimensional spaces of the initial flows, wavelet flows and main flows are introduced. These spaces are associated with the original and the enlarged grids, respectively. Estimates for the duration of the calculations are given with taking into account the properties of a communication computer environment. The presentation is accompanied with illustrative examples. We consider the grid functions whose domain is a grid on the real axis (for example, on the set of integers). This approach is convenient when processing flows are sequences of numbers. Then we discuss a grid enlargement and construct an embedded discrete spline space. Using a projection operator, we obtain a wavelet decomposition and give an illustration example of the mentioned decomposition. Taking into account the obtained algorithms we consider their implementation with OPS and PMS. In the situation of the unlimited concurrency the duration (runtime) of calculation with PMS does not depend on the data volume (i.e. it does not depend on the length of the initial flow), on the other hand, the duration of the calculation with OPS is directly proportional to the data volume.

AB - A discrete spline-wavelet decomposition of the first order is discussed in the framework of the nonclassical approach. The purpose of this paper is to estimate the calculation duration for the discrete spline-wavelet decomposition with the use of two sorts of computers: One-Processor System (OPS) and Parallel Multi-processor System (PMS). The main object is the grid functions, which are named flows. The finite dimensional spaces of the initial flows, wavelet flows and main flows are introduced. These spaces are associated with the original and the enlarged grids, respectively. Estimates for the duration of the calculations are given with taking into account the properties of a communication computer environment. The presentation is accompanied with illustrative examples. We consider the grid functions whose domain is a grid on the real axis (for example, on the set of integers). This approach is convenient when processing flows are sequences of numbers. Then we discuss a grid enlargement and construct an embedded discrete spline space. Using a projection operator, we obtain a wavelet decomposition and give an illustration example of the mentioned decomposition. Taking into account the obtained algorithms we consider their implementation with OPS and PMS. In the situation of the unlimited concurrency the duration (runtime) of calculation with PMS does not depend on the data volume (i.e. it does not depend on the length of the initial flow), on the other hand, the duration of the calculation with OPS is directly proportional to the data volume.

KW - Duration of calculation

KW - Parallelization

KW - Runtime

KW - Spline-wavelet decomposition

UR - http://www.scopus.com/inward/record.url?scp=85072332818&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85072332818

VL - 18

SP - 241

EP - 249

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -