@article {2019, title = {Convergence analysis of LSQR for compact operator equations}, journal = {Linear Algebra and its Applications}, volume = {583}, year = {2019}, pages = {146-164}, abstract = {

In this paper we analyze the behavior of the LSQR algorithm for the solution of compact operator equations in Hilbert spaces. We present results concerning existence of Krylov solutions and the rate of convergence in terms of an lp sequence where p depends on the summability of the singular values of the operator. Under stronger regularity requirements we also consider the decay of the error. Finally we study the approximation of the dominant singular values of the operator attainable with the bidiagonal matrices generated by the Lanczos bidiagonalization and the arising low rank approximations. Some numerical experiments on classical test problems are presented.

}, keywords = {Compact operator, Lanczos bidiagonalization, Linear ill-posed problem, LSQR}, issn = {0024-3795}, doi = {https://doi.org/10.1016/j.laa.2019.08.024}, url = {https://www.sciencedirect.com/science/article/pii/S0024379519303714}, author = {Noe Caruso and Paolo Novati} } @article {2019, title = {On Krylov solutions to infinite-dimensional inverse linear problems}, journal = {Calcolo}, volume = {56}, year = {2019}, pages = {1{\textendash}25}, abstract = {

We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of a given inverse problem, together with a series of model examples and numerical experiments.

}, author = {Noe Caruso and Alessandro Michelangeli and Paolo Novati} } @article {2018, title = {Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry}, journal = {International Journal of Mechanical Sciences}, volume = {149}, year = {2018}, pages = {481-486}, abstract = {

An elastic bilayer, consisting of an equibiaxially pre-stretched sheet bonded to a stress-free one, spontaneously morphs into curved shapes in the absence of external loads or constraints. Using experiments and numerical simulations, we explore the role of geometry for square and rectangular samples in determining the equilibrium shape of the system, for a fixed pre-stretch. We classify the observed shapes over a wide range of aspect ratios according to their curvatures and compare measured and computed values, which show good agreement. In particular, as the bilayer becomes thinner, a bifurcation of the principal curvatures occurs, which separates two scaling regimes for the energy of the system. We characterize the transition between these two regimes and show the peculiar features that distinguish square from rectangular samples. The results for our model bilayer system may help explaining morphing in more complex systems made of active materials.

}, keywords = {Bifurcation, Elastic bilayer, Pre-stretch, Shape programming}, issn = {0020-7403}, doi = {https://doi.org/10.1016/j.ijmecsci.2017.08.049}, url = {https://www.sciencedirect.com/science/article/pii/S0020740317311761}, author = {Noe Caruso and Aleksandar Cvetkovi{\'c} and Alessandro Lucantonio and Giovanni Noselli and Antonio DeSimone} } @article {2018, title = {Truncation and convergence issues for bounded linear inverse problems in Hilbert space}, number = {SISSA;50/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {We present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests.}, url = {http://preprints.sissa.it/handle/1963/35326}, author = {Noe Caruso and Alessandro Michelangeli and Paolo Novati} }