BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Back to the roots: Solving polynomial systems with numerical linea
 r algebra tools
DTSTART:20170331T101500
DTEND:20170331T111500
DTSTAMP:20260407T183821Z
UID:dc67eda20638a7468696899fcd69bdb5af04c835ecfe83d4be56277e
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Dr. Bart De Moor\nFinding the roots of a set of multivar
 iate polynomials has numerous applications in geometry and optimization\, 
 system and control theory\, modeling and identification\, statistics and b
 ioinformatics\, and many other scientific disciplines. It is an old yet fa
 scinating problem\, that has intrigued scientists throughout the ages\, st
 arting with the Greeks\, over Fermat and Descartes\, Newton\, Leibniz\, Be
 zout and many many others.\n\nIn this talk\, we will elaborate on a resear
 ch program\, the objective of which is to translate the many – symbolic 
 - algorithms from algebraic geometry\, into numerical linear algebra algeb
 ra algorithms. Our talk develops ideas on three complementary levels:\n\n	
 Geometric linear algebra\, which deals with column and row vector spaces\,
  dimensions\, orthogonality\, kernels\, eigenvalue problems and the like\n
 	Numerical linear algebra\, where we conceptually deal with tools like Gra
 m-Schmidt orthogonalization\, the singular value decomposition\, ranks\, a
 ngles between subspaces\, etc.\n	Numerical algorithms\, which implement th
 e linear algebra tools into an efficient and numerically robust method. He
 re we can exploit matrix structures (e.g. Toeplitz or sparsity)\, investig
 ate variations of iterative methods (e.g. power methods) or try to speeden
  up convergence (e.g. by FFT).\n\nOur claim is\, that in due time\, we wil
 l have a numerical linear algebra based tool set to efficiently and robust
 ly find all roots of a set of multivariate polynomials. Notions from linea
 r algebra we use are column and row spaces\, ranks\, kernels and the eigen
 value problem\, but also Grassmann’s dimension theorem and angles betwee
 n subspaces. The tool set we use are algorithms such as the QR-\, the CS- 
 and the singular value decomposition (SVD).\n\nWe will illustrate our resu
 lts with some motivating examples.
LOCATION:ME C2 405 https://plan.epfl.ch/theme/generalite_thm_v2?request_lo
 cale=en&room=me%20c2%20405&domain=places&dim_floor=2&lang=en&dim_lang=en&b
 aselayer_ref=grp_backgrounds&tree_groups=centres_nevralgiques%2Cacces%2
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR