Multidimensional Polynomial Splines
This paper showcases the study of multidimensional polynomial splines viewing them from a signal processing perspective. Combining the advantages of the tabular-algorithmic methods and using them for reproduction of functions and multidimensional B-splines lead to the implementation of parallel-pipeline multivariable computation structures that ensure the highest performance. Multiple multiprocessor high-performance computation structures were evaluated based on tabular-algorithmic method of processing known for top-speed and multidimensional spline approximation renowned for high performance. A parallel-pipeline computation structure was developed to implement two-dimensional basic spline approximation. This saves memory for storage of values of basic splines twice on a limited number of processors. A parallel-pipeline computation structure is proposed for recovering values of three-variable functions that have a limited number of processors and are noted for high performance. Some main characteristics of the implementation of tabular-algorithmic computation structures were obtained for processing of signals in piecewise-polynomial basics. It was proven that the tabular-algorithmic computation structures based on basic splines function faster classical polynomials of the same levels. Parabolic basic splines are 1.76 times faster and cubic basic splines 2.53 times faster than their respective classic counterparts. It has been proven that the hardware costs for implementation of the computation structures based on cubic splines are higher at the same time.
- 3.I. Garcia Marco, P. Koiran, T. Pecatte, Polynomial equivalence problems for sum of affine powers. PRoceddInt3rpp 303–310, (2018). https://doi.org/10.1145/3208976.3208993