


Courses
Minimizing communication in numerical linear algebra
Nonlinear eigenvalue problems: analysis and numerical solution Volker Mehrmann, Technische Universitat Berlin, Germany.
Nonlinear eigenvalue problems arise in a huge number of applications ranging from classical mechanics, i.e. the vibration of structures or vehicles, acoustics, to the simulation of quantum dots. In this course several major applications and the basic theory of nonlinear eigenvalue problems will be discussed. This includes linearization techniques for polynomial eigenvalue problems that have recently been revised in the particular context of preserving given structures. We then discuss the most important techniques for the numerical solution of polynomial and general nonlinear eigenvalue problems as well as the conditioning and perturbation theory.
From Matrix to Tensor: The Transition to Computational Multilinear Algebra Charles Van Loan, Cornell University, Ithaca, New York, USA.
Highdimensional modeling is becoming ubiquitous across the sciences and engineering creating a demand for informative tensorbased computation. A tensor can be regarded as a multisubscripted matrix. What does it mean to say that an n_{1}xn_{2}xn_{3} tensor has low rank and how might it be estimated? Can we reshape a 2^{100} vector into a tensor that has a sparse representation? Does the singular value decomposition of a flattened tensor tell us anything about the original data set? All these questions lead to challenging problems in numerical linear algebra that will be covered in this short course. Our goal is to portray tensor computation as the next big thing in scientific computing, where reasoning about algorithms has already progressed from the level of scalars to the level of matrices to the level of block matrices.
Linear Algebra and Optimization Margaret H. Wright, Courant Institute, New York University, USA.
For more than 60 years, starting with the simplex method for linear programming, the heart of many computational optimization methods has consisted of one or more linear algebraic subproblems. Very often these are linear systems, symmetric and unsymmetric, ranging from small to large and dense to sparse. In addition, some optimization techniques depend on linear least squares, calculation or estimation of eigenvalues/vectors and singular values/vectors, and updating matrix factorizations. This course will examine the highlights of twoway connections between linear algebra and optimization, including recent applications in largescale simulation and theoretical computer science.
