A Programming Methodology for Designing Block Recursive Algorithms

In this paper, we use the tensor product notation as the framework of a programming methodology for designing block recursive algorithms. We first express a computational problem in its matrix form. Next, we formulate a matrix equation for the matrix of the computational problem. Then, try to find a solution of the matrix equation such that the solution is composed of simple matrices. Finally, we recursively factorize the subproblem to obtain a tensor product formula representing an algorithm for the given problem. In this methodology, operations of a tensor product formula can be mapped to language constructs of high-level programming languages. That is, we can generate computer programs, including programs for parallel computers and distributed-memory multiprocessors, from tensor product formulas. We will use the parallel prefix problem and the discrete Fourier transform problem as examples to illustrate the methodology and derive various parallel prefix and fast Fourier transform a...

• Type: Journal
• Year: 2006
• Where: JISE
• Authors: Min-Hsuan Fan, Chua-Huang Huang, Yeh-Ching Chung, Jen-Shiuh Liu, Jei-Zhii Lee
• Keywords: Computational Problem, JISE 2006, Tensor Product, Tensor Product Formulas