01277nas a2200193 4500008004100000022001400041245006400055210006400119300001200183490000800195520068500203653002100888653003000909653002900939653000900968100001600977700001800993856007201011 2019 eng d a0024-379500aConvergence analysis of LSQR for compact operator equations0 aConvergence analysis of LSQR for compact operator equations a146-1640 v5833 a
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.
10aCompact operator10aLanczos bidiagonalization10aLinear ill-posed problem10aLSQR1 aCaruso, Noe1 aNovati, Paolo uhttps://www.sciencedirect.com/science/article/pii/S002437951930371400835nas a2200145 4500008004100000245007200041210006800113300001100181490000700192520032300199100001600522700002900538700001800567856010400585 2019 eng d00aOn Krylov solutions to infinite-dimensional inverse linear problems0 aKrylov solutions to infinitedimensional inverse linear problems a1–250 v563 aWe 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.
1 aCaruso, Noe1 aMichelangeli, Alessandro1 aNovati, Paolo uhttps://www.math.sissa.it/publication/krylov-solutions-infinite-dimensional-inverse-linear-problems01712nas a2200229 4500008004100000022001400041245010200055210006900157300001200226490000800238520097600246653001601222653002001238653001601258653002201274100001601296700002701312700002701339700002201366700002201388856007201410 2018 eng d a0020-740300aSpontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry0 aSpontaneous morphing of equibiaxially prestretched elastic bilay a481-4860 v1493 aAn 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.
10aBifurcation10aElastic bilayer10aPre-stretch10aShape programming1 aCaruso, Noe1 aCvetković, Aleksandar1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://www.sciencedirect.com/science/article/pii/S0020740317311761