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RICAM Colloquium - Han Cheng Lie

Han Cheng Lie, Universität Potsdam - Title: A class of rank-constrained operator approximation problems and some applications

March 06, 2025, 15:30, SP2 416-2

ABSTRACT: A classical problem is to find a matrix X that best approximates a given matrix M, subject to the constraint that the approximating matrix X has at most rank r. We present a generalisation of this problem, first in the matrix setting and then in the linear operator setting. We then propose some solutions to the problem in the operator setting and consider properties of the solutions, such as continuity and being 'minimal' in an appropriate sense, and consider applications to linear operator learning and to Bayesian inverse problems. 

Joint work with Giuseppe Carere (U. Potsdam).

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