日時： 2016年8月5日(金) 14:30～15:30
場所： 東京大学工学部 14号館 5階 534
講演者： 中務 佑治 (University of Oxford)
題目： Best L1 Polynomial Approximation
An important observation in compressed sensing is the exact recovery of
an l0 minimizer to an underdetermined linear system via the l1
minimizer, given the knowledge that a sparse solution vector exists.
Here, we develop a continuous analogue of this observation and show that
the best L1 and L0 polynomial approximants of a corrupted function
(continuous analogue of sparse vectors) are equivalent. We use this to
construct best L1 polynomial approximants of corrupted functions via
linear programming. We also present a numerical algorithm for computing
best L1 polynomial approximants to general continuous functions, and
observe that compared with best L-infinity and L2 polynomial
approximants, the best L1 approximants tend to have error functions that
are more localized.
This is joint work with Alex Townsend (MIT).