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Introduction to Parallel Computing, Second Edition by Vipin Kumar, George Karypis, Anshul Gupta, Ananth Grama

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Chapter 8. Dense Matrix Algorithms

Algorithms involving matrices and vectors are applied in several numerical and non-numerical contexts. This chapter discusses some key algorithms for dense or full matrices that have no or few known usable zero entries. We deal specifically with square matrices for pedagogical reasons, but the algorithms in this chapter, wherever applicable, can easily be adapted for rectangular matrices as well.

Due to their regular structure, parallel computations involving matrices and vectors readily lend themselves to data-decomposition (Section 3.2.2). Depending on the computation at hand, the decomposition may be induced by partitioning the input, the output, or the intermediate data. Section 3.4.1 describes in detail the ...

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