18 citations · 30 across the 10 of their papers we have counts for
11 papers
Harmonic Measures and Numerical Computation of Cauchy Problems for Laplace Equations
Yu Chen, Jin Cheng, Shuai Lu +1
It is well known that Cauchy problem for Laplace equations is an ill-posed problem in Hadamard's sense. Small deviations in Cauchy data may lead to large errors in the solutions. I…
Increasing stability of a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds
Shuai Lu, Jian Zhai
We consider the problem of recovering a nonlinear potential function in a nonlinear Schrödinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neu…
Increasing stability of the first order linearized inverse Schrödinger potential problem with integer power type nonlinearities
Sen Zou, Shuai Lu, Boxi Xu
We investigate the increasing stability of the inverse Schrödinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order li…
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities
Shuai Lu, Mikko Salo, Boxi Xu
We consider increasing stability in the inverse Schrödinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to sm…
Determination of source terms in diffusion and wave equations by observations after incidents: uniqueness and stability
Jin Cheng, Shuai Lu, Masahiro Yamamoto
We consider a diffusion and a wave equations: with the zero initial and boundary conditions, where…
On the asymptotical regularization for linear inverse problems in presence of white noise
Shuai Lu, Pingping Niu, Frank Werner
We interpret steady linear statistical inverse problems as artificial dynamic systems with white noise and introduce a stochastic differential equation (SDE) system where the inver…
An inverse conductivity problem in multifrequency electric impedance tomography
Jin Cheng, Mourad Choulli, Shuai Lu
We deal with the problem of determining the shape of an inclusion embedded in a homogenous background medium. The multifre-quency electrical impedance tomography is used to image t…
Linearized inverse Schrödinger potential problem at a large wavenumber
Victor Isakov, Shuai Lu, Boxi Xu
We investigate recovery of the (Schrödinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a Hölder typ…
Tikhonov regularization with l^0-term complementing a convex penalty: l^1 convergence under sparsity constraints
Wei Wang, Shuai Lu, Bernd Hofmann +1
Measuring the error by an l^1-norm, we analyze under sparsity assumptions an l^0-regularization approach, where the penalty in the Tikhonov functional is complemented by a general…
Analysis of regularized Nyström subsampling for regression functions of low smoothness
Shuai Lu, Peter Mathé, Sergiy Pereverzyev
This paper studies a Nyström type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproduc…
Filter Based Methods For Statistical Linear Inverse Problems
Marco A. Iglesias, Kui Lin, Shuai Lu +1
Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse…