Fast and practical parallel polynomial interpolation

Technical Report · Thu Jan 01 00:00:00 EST 1987

OSTI ID:5545183

Egecioglu, O; Gallopoulos, E; Koc, C K

We present fast and practical parallel algorithms for the computation and evaluation of interpolating polynomials. The algorithms make use of fast parallel prefix techniques for the calculation of divided differences in the Newton representation of the interpolating polynomial. For n + 1 given input pairs the proposed interpolation algorithm requires 2 (log (n + 1)) + 2 parallel arithmetic steps and circuit size O(n/sup 2/). The algorithms are numerically stable and their floating-point implementation results in error accumulation similar to that of the widely used serial algorithms. This is in contrast to other fast serial and parallel interpolation algorithms which are subject to much larger roundoff. We demonstrate that in a distributed memory environment context, a cube connected system is very suitable for the algorithms' implementation, exhibiting very small communication cost. As further advantages we note that our techniques do not require equidistant points, preconditioning, or use of the Fast Fourier Transform. 21 refs., 4 figs.

• Research Organization: Illinois Univ., Urbana (USA). Center for Supercomputing Research and Development
• DOE Contract Number: W-7405-ENG-48; FG02-85ER25001
• OSTI ID: 5545183
• Report Number(s): DOE/ER/25001-89; CSRD-646; ON: DE88003530
• Resource Relation: Other Information: Portions of this document are illegible in microfiche products
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
POLYNOMIALS
INTERPOLATION
PARALLEL PROCESSING
ALGORITHMS
ERRORS
NEWTON METHOD
USES
FUNCTIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
PROGRAMMING
990230* - Mathematics & Mathematical Models- (1987-1989)
990210 - Supercomputers- (1987-1989)