Time: |
14:15-18:00 |
Venue: |
FSC1217, Fong Shu Chuen Building,
Ho Sin Hang Campus, Hong Kong Baptist University |
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| Speakers: |
| Claude Brezinski (University of Sciences and Technologies of Lille, France) |
| Raymond Chan (The Chinese University of Hong Kong) |
| Walter Gander (ETH, Switzerland) |
| Michael Ng (Hong Kong Baptist University) |
| Michela Redivo Zaglia (Universit degli Studi di Padova, Italy)
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| Program | |
| 14:15-15:00 |
Claude Brezinski
Survey on some extrapolation methods for linear algebra problems
(abs)
Many methods used in numerical linear algebra are iterative. Quite often, the sequence they produce converge slowly, thus restricting their practical use. This talk
will present a survey of methods for their acceleration: sequence transformations, extrapolation methods, projection methods. Then, some specific applications will be
discussed: estimation of the norm of the error, Tikhonov's regularization, traces of matrix powers. |
| 15:00-15:45 |
Raymond Chan
Linearized alternating direction method for constrained linear least-squares problem
(abs)
We apply the alternating direction method (ADM) to
solve a constrained linear least-squares problem where the objective
function is a sum of two least-squares terms and the constraints are
box constraints. Using ADM, we decompose the original problem into
two easier least-squares subproblems at each iteration. To speed up
the inner iteration, we linearize the subproblems whenever their
closed-form solutions do not exist. We prove the convergence of the
resulting algorithm and apply it to solve some image deblurring
problems where the matrices involved are structured matrices.
We show the efficiency of our algorithm by comparing it
with Newton-type methods. Extension to TV-type problems will also
be discussed.
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| 15:45-16:00 |
Coffee Break |
| 16:00-16:45 |
Walter Gander
Generating numerical algorithms using computer algebra
(abs)
We show how numerical algorithms can be derived in a simple way using
computer algebra. Examples are numerical differentiation, quadrature
and multi-step methods for ODE. It is also shown how the
discretization error of a method can be computed automatically. This
approach not only makes formularies obsolete (in fact some errors were
found in Abramowitz/Stegun) but is also useful in teaching since
principles and fundamentals are emphasized and we can leave the
sometimes tedious derivation of the specific algorithm to the machine.
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| 16:45-17:30 |
Michela Redivo-Zaglia
The PageRank algorithm for web search (abs)
The PageRank algorithm was designed by Brin and Page to classify the pages on internet according to
their relevance to keywords. After explaining the basic ideas of this algorithm, some of its properties are analyzed. Its implementation is discussed. Since the
computation of the PageRank vector which contains
the ranks of the pages in decreasing order of relevance is iterative and converges slowly, we present some procedures for its acceleration. Polynomial and rational
approximations to the PageRank vector are also proposed. Numerical examples end the talk.
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| 17:30-18:00 |
Michael Ng
MultiRank and HAR algorithms for ranking multi-relational data
(abs)
In this talk, we extend PageRank algorithm to MultiRank and HAR algorithms
to deal with query search for multi-relational data.
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Host:
Centre for Mathematical Imaging and Vision, Hong Kong Baptist
University
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