Numerical Analysis

Taking Advantage of Degeneracy in Cone Optimization: with Applications to Sensor Network Localization

Author: 
Henry Wolkowicz
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
Taking Advantage of Degeneracy in Cone Optimization: with Applications to Sensor Network Localization

Solving linear systems by orthogonal tridiagonalization (GMINRES and/or GLSQR)

Author: 
Michael Saunders
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
A general matrix A can be reduced to tridiagonal form by orthogonal transformations on the left and right: UTAV = T. We can arrange that the rst columns of U and V are proportional to given vectors b and c. An iterative form of this process was given by Saunders, Simon, and Yip (SINUM 1988) and used to solve square systems Ax = b and ATy = c simultaneously. (One of the resulting solvers becomes MINRES when A is symmetric and b = c.) The approach was rediscovered by Reichel and Ye (NLAA 2008) with emphasis on rectangular A and least-squares problems Ax ~ b. The resulting solver was regarded as a generalization of LSQR (although it doesn't become LSQR in any special case). Careful choice of c was shown to improve convergence. In his last year of life, Gene Golub became interested in \GLSQR" for estimating cTx = bTy without computing x or y. Golub, Stoll, and Wathen (ETNA 2008) revealed that the orthogonal tridiagonalization is equivalent to a certain block Lanczos process. This reminds us of Golub, Luk, and Overton (TOMS 1981): a block Lanczos approach to computing singular vectors.
Notes: 

On solving indefinite least squares problems via anti-triangular factorizations

Author: 
Paul Van Dooren
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
On solving indefinite least squares problems via anti-triangular factorizations: Nicola Mastronardi, IAC-CNR, Bari, Italy and Paul Van Dooren, UCL, Louvain-la-Neuve, Belgium

Eigenvalue avoided crossings

Author: 
Nick Trefethen
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
Eigenvalue avoided crossings

Communication-­ Avoiding Algorithms for Linear Algebra and Beyond

Author: 
James Demmel
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
Communication-­ Avoiding Algorithms for Linear Algebra and Beyond

The Higher Order Generalized Singular Value Decomposition

Author: 
Charles Van Loan
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
Suppose you have a collection of data matrices each of which has the same number of columns. The HO-GSVD can be used to identify common features that are implicit across the collection. It works by identifying a certain (approximate) invariant subspace of a matrix that is a challenging combination of the collection matrices. In describing the computational process I will talk about the Higher Order CS decomposition and a really weird optimization problem that I bet you have never seen before! Joint work with Orly Alter, Priya Ponnapalli, and Mike Saunders.

Convex Optimization for Finding Influential Nodes in Social Networks

Author: 
Steve Vavasis
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
Convex Optimization for Finding Influential Nodes in Social Networks. Joint work with Lisa Elkin and Ting Kei Pong of Waterloo.

Relaxations for some NP-hard problems based on exact subproblems

Author: 
Franz Rendl
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
Relaxations for some NP-hard problems based on exact subproblems. Joint work with E. Adams, M. Anjos (Montreal) and A. Wiegele (Klagenfurt).

Differential equations for the approximation of the distance to the closest defective matrix

Author: 
Nicola Gugliemi
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
Differential equations for the approximation of the distance to the closest defective matrix. Joint work with P. Butta' and S. Noschese (Università di Roma La Sapienza) and M. Manetta (Università dell'Aquila).

H2 optimal model order reduction for parametric systems using RBF metamodels

Author: 
Sarah Grundel
Date: 
Thu, Aug 8, 2013 - Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Abstract: 
Model Order Reduction Methods for linear systems are well studied and many successful methods exist. We will review some and explain more recent advances in Parametric Model Order Reduction. The focus will be on methods where we interpolate certain signi cant measures, that are computed for speci c values of the parameter by Radial Basis Function Interpolation. These measures have a disadvantage as they behave like eigenvalues of matrices depending on parameters and we will explain how that can be dealt with in practice. We will furthermore need to introduce a technique to create a medium size model.
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