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Chapter
Parallel Computing
Despite five decades of research, parallel computing remains an exotic, frontier technology on the fringes of mainstream computing. Its much-heralded triumph over sequential computing has yet to materialize. T...
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Chapter
Review of Matrix Factorization
Matrix factorization algorithms lie at the heart of many signal processing applications. For example, the problem of finding a vector x, such that Ax = b, where A is an m × n complex matrix and b is a complex n-l...
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Chapter
Case Study 2: Parallel Compact WY QR Factorization
During the past five years the widespread availability of tuned kernels for performing matrix-matrix multiplication has dramatically narrowed the focus of parallel algorithm research in the field of linear alg...
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Chapter
Conclusion
Despite decades of research in industry and academia, parallel algorithm design largely remains an art form. The systematic steps in the Parallel Algorithm Synthesis Procedure provide algorithm designers with ...
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Chapter
Introduction
Parallel computing is the only viable, cost-effective approach to meeting the timing constraints of many high performance signal processing applications. The computational and/or I/O requirements of a single a...
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Chapter
Parallel Algorithm Synthesis Procedure
The Parallel Algorithm Synthesis Procedure introduces parameters to control the partitioning and scheduling of computation and communication. The goal is to design and implement parameterized software componen...
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Chapter
Case Study 3: Parallel Matrix Bidiagonalization
Bidiagonal factorization is the first step in solution procedures for computing the singular values of a matrix A ∈ R m×n (Demmel and Kahan, 1990; Golub and Van Loan, 1989).
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Chapter
Case Study 1: Parallel Fast Givens QR Factorization
Although parallel QR factorization has been the topic of much research, available parallel algorithms exhibit poor scalability characteristics on matrices with dimensions less than 3000. As a consequence, ther...
