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generalizedsmoothingsplines.jl's Introduction

Hi there ๐Ÿ‘‹

I am currently doing a 1-year PostDoc at the Section for Scientific Computing at the Technical University of Denmark. Here I look into efficient implementations of interior-point methods for a certain applications in civil engineering. Previously I was a PhD student in the Acoustic Technology Group (ACT) as well as The Centre for Acoustic-Mechanical Micro Systems (CAMM). Before this I studied computational science and engineering with an emphasis on optimization methods and numerical analysis. In particular I took an interest in rank structured approaches which lead me down the path of studying Boundary Integral Equations applied to acoustics.

Things I deal with on a regular basis

  • Boundary Integral Equations (and their solution through the Boundary Element Method using Fast Multipole Methods and $\mathcal{H}$-matrices).
  • Structured linear algebra (specifically rank structure and sparsity).
  • Optimization algorithms (mostly interior point methods).

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generalizedsmoothingsplines.jl's Issues

Adding support for shape restricted smoothing splines

Current unknowns for shape restricted curves

  • How do compute optimal roughness parameter. Currently we just compute optimal $\lambda$ from the unconstrained problem.
  • How to compute/interpret uncertainties.

Currently the derivatives are computed using finite differences. I believe that we should be able to directly differentiate the spline directly (it is just a linear combination of kernels, which should be differentiable?).

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