Digital Signal Processing Handbook P10

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Digital Signal Processing Handbook P10

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Yagle, A.E. “Fast Matrix Computations” Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton: CRC Press LLC, 1999 c 1999 by CRC Press LLC .10 Fast Matrix Computations 10.1 Introduction 10.2 Divide-and-Conquer Fast Matrix Multiplication Strassen Algorithm • Divide-and-Conquer • Arbitrary Precision Approximation (APA) Algorithms • Number Theoretic Transform (NTT) Based Algorithms Overview • The Wavelet Transform • Wavelet Representations of Integral Operators • Heuristic Interpretation of Wavelet Sparsification 10.3 Wavelet-Based Matrix Sparsification Andrew E. Yagle University of Michigan References 10.1 Introduction This chapter presents two major approaches to fast matrix multiplication. We restrict our attention to matrix multiplication, excluding matrix addition and matrix inversion, since matrix addition...

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