Pointwise error estimates in localization microscopy

Pointwise error estimates in localization microscopy

Pointwise localization of individual fluorophores is a critical step in super-resolution localization microscopy and single particle tracking. Although the methods are limited by the localization errors of individual fluorophores, the pointwise localization precision has so far been estimated using theoretical best case approximations that disregard, for example, motion blur, defocus effects an...

Pointwise localized error estimates for parabolic finite element equations

Pointwise Error Estimates for Relaxation Approximations to Conservation Laws

We obtain sharp pointwise error estimates for relaxation approximation to scalar conservation laws with piecewise smooth solutions. We first prove that the first-order partial derivatives for the perturbation solutions are uniformly upper bounded (the so-called Lip+ stability). A one-sided interpolation inequality between classical L1 error estimates and Lip+ stability bounds enables us to conv...

Pointwise RMS bias error estimates for design of experiments

Response surface approximations offer an effective way to solve complex problems. However limitations on computational expense pose restrictions to generate ample data and a simple model is typically used for approximation leaving the possibility of errors due to insufficient model known as bias errors. This paper presents a method to estimate pointwise RMS bias errors in response surface model...

Sharply local pointwise a posteriori error estimates for parabolic problems

We prove pointwise a posteriori error estimates for semiand fullydiscrete finite element methods for approximating the solution u to a parabolic model problem. Our estimates may be used to bound the finite element error ‖u−uh‖L∞(D), where D is an arbitrary subset of the space-time domain of definition of the given PDE. In contrast to standard global error estimates, these estimators de-emphasiz...