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VERSION:2.0
PRODID:-//Memento EPFL//
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SUMMARY:Computation graph for matrix functions
DTSTART:20211026T161500
DTEND:20211026T171500
DTSTAMP:20260407T051232Z
UID:a46ab80d85119dbbefc03e7799d2e21859fea6c1c0d06bc52f5bfc0c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Elias Jarlebring\, KTH\nMatrix functions\, such as the matrix 
 exponential\, matrix square root\, the sign-function\, are fundamental con
 cepts that appear in wide range of fields in science and technology. In th
 is talk\, the evaluation of matrix functions is viewed as a computational 
 graphs. More precisely\, by viewing methods as directed acyclic graphs (DA
 Gs) we can improve and analyze existing techniques them\, and derive new m
 ore efficient algorithms. The accuracy of these matrix techniques can be c
 haracterized by the accuracy of their scalar counterparts\, thus designing
  algorithms for matrix functions can be treated as a scalar-valued optimiz
 ation problem. The derivatives needed during the optimization can be calcu
 lated automatically by exploiting the structure of the DAG\, in a fashion 
 analogous to backpropagation. These functions and many more features are i
 mplemented in GraphMatFun.jl\, a Julia package that offers the means to ge
 nerate and manipulate computational graphs\, optimize their coefficients\,
  and generate Julia\, MATLAB\, and C code to evaluate them efficiently at 
 a matrix argument. The software also provides tools to estimate the accura
 cy (including backward error) of a graph-based algorithm and thus obtain n
 umerically reliable methods. For the exponential\, for example\, using a p
 articular form (degree-optimal) of polynomials produces implementations th
 at in many cases are cheaper\, in terms of computational cost\, than the P
 adé-based techniques typically used in mathematical software. The optimiz
 ed graphs and the corresponding generated code are available online.
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
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