Yousef Saad Department Of Computer Science And Engineering

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Introduction Numerical linear algebra has always been a “universal” tool in science and engineering. Its focus has changed over the years to tackle “new challenges” 1940s–1950s: Major issue: the flutter problem in aerospace engineering. Focus: eigenvalue problem. ➤ Then came the discoveries of the LR and QR algorithms, and the package Eispack followed a little later 1960s: Problems related to the power grid promoted what we know today as general sparse matrix techniques. Late 1980s – 1990s: Focus on parallel matrix computations. Late 1990s: Big spur of interest in “financial computing” [Focus: Stochastic PDEs] CSE Colloquium 11/09/09 p. 2
➤ Then the stock market tanked .. and numerical analysts returned to more mundaine basics Recent/Current: Google page rank, data mining, problems related to internet technology, knowledge discovery, bio-informatics, nano-technology, ... ➤ Major new factor: Synergy between disciplines. Example: Discoveries in materials (e.g. semi conductors replacing vacuum tubes in 1950s) lead to faster computers, which in turn lead to better physical simulations.. ➤ What about data-mining and materials? ➤ Potential for a perfect union... CSE Colloquium 11/09/09 p. 3
Page 1: From data-mining to nanotechnology
Page 5 and 6: Electronic structure ➤ Quantum me
Page 7 and 8: ➤ Hamiltonian H is of the form :
Page 9 and 10: The underlying physical laws necess
Page 11 and 12: Kohn-Sham equations → nonlinear e
Page 13 and 14: The physical domain CSE Colloquium
Page 15 and 16: CHEBYSHEV FILTERING
Page 17 and 18: Chebyshev Subspace iteration - expe
Page 19 and 20: NUMERICAL LINEAR ALGEBRA IN DATA MI
Page 21 and 22: Major tool of Data Mining: Dimensio
Page 23 and 24: Linear Dimensionality Reduction Giv
Page 25 and 26: 2-D ‘reductions’: 15 10 5 0 −
Page 27 and 28: 2-D ’reductions’: 6 4 2 0 −2
Page 29 and 30: Sparse Matrices viewpoint * Joint w
Page 31 and 32: Supervised learning: classification
Page 33 and 34: A harder case: 4 3 2 1 0 −1 −2
Page 35 and 36: Fisher’s Linear Discriminant Anal
Page 37 and 38: ➤ Project set on a one-dimensiona
Page 39 and 40: Trace ratio problem * Joint work wi
Page 41 and 42: Background: The Lanczos procedure A
Page 43 and 44: Information Retrieval: Vector Space
Page 45 and 46: Common approach: Use the SVD ➤ Ne
Page 47 and 48: Polynomial filters - examples Appro
Page 49 and 50: IR: Use of the Lanczos algorithm (1
Page 51 and 52: ➤ Theory well understood: works w
Page 53 and 54:
Average query times average query t
Page 55 and 56:
In summary: ➤ Results comparable
Page 57 and 58:
Difficulty Positions, Expressions,
Page 59 and 60:
Tests: Face Recognition Tests with
Page 61 and 62:
GRAPH-BASED METHODS
Page 63 and 64:
Example: The Laplacean eigenmaps La
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A unified view * Joint work with Ef
Page 67 and 68:
Graph-based methods in a supervised
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Repulsion Laplaceans * Joint work w
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Materials informatics at work. Illu
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Conclusion ➤ Many, many, interest
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Yousef Saad Department Of Computer Science And Engineering

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