Overview of QUIC-SVD - UMass Graphics Lab - University of ...

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Parallelize Gram Schmidt Orthogonalization • Modified Gram Schmidt: r r proj( r, v ), 1 1 r r proj( r , v ), 2 1 1 2 ... ... r r r proj( r , v ) v r r n1 k k 1 k 1 k • This has good numerical stability, but is hard to parallelize, as the computation is sequential! 22
Parallelize Gram Schmidt Orthogonalization • Our approach: Blocked Gram Schmidt (1) v v proj v u1 proj v u2 proj v um ( , ) ( , ) ... ( , ) v v proj( v , u ) proj( v , u ) ... proj( v , u ) (2) (1) (1) (1) (1) m1 m2 2m ...... u v proj( v , u ) proj( v , u ) ... proj( v , u ) ( n/ m) ( n/ m) ( n/ m) ( n/ m) k 1 2m1 2m2 k • This hybrid approach combines the advantages <strong>of</strong> the previous two – numerically stable, and GPU-friendly. 23
Page 1 and 2: A GPU-based Approximate SVD Algorit
Page 3 and 4: Introduction • Approximate SVD
Page 5 and 6: Introduction • Sample-based Appro
Page 7 and 8: Our Goal • Map QUIC-SVD onto the
Page 9 and 10: Our Work • A CUDA implementation
Page 11 and 12: Overview of QUIC-SVD [Holmes et al.
Page 17 and 18: Overview of QUIC-SVD • Monte Carl
Page 19 and 20: GPU Implementation of QUIC-SVD •
Page 21: Parallelize Gram Schmidt Orthogonal
Page 25 and 26: Extract the Final Result • Input:
Page 27 and 28: … … … … Partitioned QUIC-SV
Page 29 and 30: Partitioned QUIC-SVD 29
Page 31 and 32: Implementation Details • Main imp
Page 33 and 34: Performance • Comparisons: 1. Mat
Page 35 and 36: Performance - Speedup Factors 35
Page 37 and 38: Performance - CPU vs. GPU QUIC-SVD
Page 39 and 40: Integration with Manifold Alignment
Page 41 and 42: Future Work • Be able to process

Overview of QUIC-SVD - UMass Graphics Lab - University of ...

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