Sébastien Bossu, UNC Charlotte

**Title**: “Least-squares function approximation and single-pair Gram matrices”

**Abstract**: Least-squares optimization techniques can be applied to approximate a function f(x) by a line (similar to linear regression in statistics), Fourier cosines, or ReLU functions. In the first part of this talk, we will review the theory of least-squares function approximation and see how Gram matrices (covariance matrices in statistics) play an important role. In the second part of this talk, I will present my recent results about the inverse sum of two single-pair matrices corresponding to the Gram matrix of a system of ReLU functions.

The first part of this talk is educational and graduate students are encouraged to attend.