Yousef Saad Department Of Computer Science And Engineering

More documents

Recommendations

Info

Diagonalization via Chebyshev filtering Given a basis [v1, . . . , vm], ’fil- ˆvi = pk(A)vi ter’ each vector as ➤ pk = Low deg. polynomial. Dampens unwanted components ➤ Filtering step not used to compute eigenvectors accurately ➤ In effect: SCF & diagonalization loops merged Convergence well preserved 1 0.8 0.6 0.4 0.2 0 Deg. 8 Cheb. polynom., on interv.: [−11] −1 −0.5 0 0.5 1 Yunkai Zhou, Y.S., Murilo L. Tiago, and James R. Chelikowsky, Phys. Rev. E, vol. 74, p. 066704 (2006). CSE Colloquium 11/09/09 p. 16
Chebyshev Subspace iteration - experiments ➤ A large calculation: Si9041H1860, using 48 processors [SGI Altix, Itanium proc., 1.6 GHz] ➤ Hamiltonian size=2, 992, 832, Num. States= 19, 015. # A ∗ x # SCF total eV /atom 1st CPU total CPU 4804488 18 -92.00412 102.12 hrs. 294.36 hrs ➤ Calculation done in ∼ 2006. ➤ Largest one done in 1997: Si525H276 ➤ Took a few days [48 h. cpu] on 64PE - Cray T3D. ➤ Now 2 hours on 1 PE (!) CSE Colloquium 11/09/09 p. 17
Page 1 and 2: From data-mining to nanotechnology
Page 3 and 4: ➤ Then the stock market tanked ..
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: CHEBYSHEV FILTERING
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
Page 65 and 66: A unified view * Joint work with Ef
Page 67 and 68:
Graph-based methods in a supervised
Page 69 and 70:
Repulsion Laplaceans * Joint work w
Page 71 and 72:
Materials informatics at work. Illu
Page 73 and 74:
Conclusion ➤ Many, many, interest
show all

Yousef Saad Department Of Computer Science And Engineering

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?