Fast computation of divided differences and parallel hermite interpolation
Journal of Complexity
Programming from specifications
Programming from specifications
An introduction to parallel algorithms
An introduction to parallel algorithms
Lagrange interpolation on a processor tree with ring connections
Journal of Parallel and Distributed Computing
Models and languages for parallel computation
ACM Computing Surveys (CSUR)
A New Network Topology with Multiple Meshes
IEEE Transactions on Computers
An axiomatic basis for computer programming
Communications of the ACM
A Discipline of Programming
Parallel Lagrange Interpolation on the Star Graph
IPDPS '00 Proceedings of the 14th International Symposium on Parallel and Distributed Processing
On Data Distributions in the Construction of Parallel Programs
The Journal of Supercomputing
Multi-mesh of trees with its parallel algorithms
Journal of Systems Architecture: the EUROMICRO Journal
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The paper presents parallel algorithms for Lagrange and Hermite interpolation methods formally derived from specifications, and using set-distributions. Set-distributions are based on set-valued mappings, and they assign a data object to more than one process. The derivation from specifications assures the correctness, and the set-distributions assure the efficiency of the programs. The obtained parallel algorithms have very good time complexities and speeds-up, and they are also cost-efficient. We consider the number of processes p to be a parameter of the algorithms, so, bounded parallelism is considered. The derivation of the algorithms is not ruled by any particular interconnection network. The possible mappings on different networks could be evaluated. The performance analysis is done considering a full-connected network, and other two interconnection networks: hypercube and multi-mesh hypercube, which preserve the cost-efficiency of the algorithms.