This minisymposium focuses on the development of numerical algorithms for multilinear algebra — a topic that is expected to have far-reaching applications in science and engineering, through both the creation of new scientific computing models and the analysis of data with nonlinear structures. The name Numerical Multilinear Algebra is not as yet in common usage. We broadly define this as the study and use of tensors/multilinear algebra, symmetric tensors/symmetric algebra, alternating tensors/exterior algebra, spinors/Clifford algebra in computational mathematics. A fundamental object of interest will be tensors. An order-k tensor may be either regarded as (1) a k-dimensional array of real/complex numbers on which algebraic operations generalizing analogous operations on matrices are defined, or (2) a linear combination of outer products of vectors. A matrix is then synonymous with a tensor of order 2. Special types of tensors such as symmetric and alternating tensors (arising from, say, cumulants and differential forms), Kronecker products of operators, are also of central importance. More specifically, this minisymposium will focus on numerical computations involving these multilinear objects, their surprising connections to questions regarding computational complexity and numerical stability, as well as the growing importance and increasing ubiquity of multilinearity in scientific and engineering applications.
This minisymposium is to be held as a part of the 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), which takes place quadrennially and is the biggest event in applied mathematics. ICIAM 2007 will be held at the Swiss Federal Institute of Technology (ETH) in Zürich, Switzerland from July 16–20, 2007.
Pierre Comon, Lieven De Lathauwer, Gene Golub, Lek-Heng Lim
The ICIAM program is now online. Our minisymposium will take place on Tuesday, July 17.
First Session: Tuesday, July 17, 11:15am–1:15pm
|Eugene Tyrtyshnikov||Russian Academy of Sciences||Fast Multilinear Approximation: a new generation of numerical algorithms|
|Boris Khoromskij||Max Planck Institute||Tensor-Product Decomposition in Computational Physics|
|Gregory Beylkin||University of Colorado at Boulder||Separated Representations and Nonlinear Approximations for Fast Algorithms in High Dimensions|
|Inderjit Dhillon||University of Texas at Austin||Fast Newton-type Methods for Nonnegative Tensor Approximation Problems|
Second Session: Tuesday, July 17, 3:45am–5:45pm
|Dario Bini||University of Pisa||The Role of Tensor Rank in the Complexity Analysis of Bilinear Forms|
|Orly Alter||University of Texas at Austin||Tensor Computations for Genomic Signal Processing|
|Douglas Arnold||University of Minnesota at Twin Cities||Finite Element Differential Forms|
|Lek-Heng Lim||Stanford University||Multilinear Algebra in Signal Processing and Machine Learning|
For further information on this meeting, please email Pierre Comon at pcomon(at)i3s.unice.fr or Lek-Heng Lim at lekheng(at)stanford.edu
This minisymposium is partially supported by the PASCAL European Network of Excellence (PASCAL — Pattern Analysis, Statistical Modelling, and Computational Learning).