Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

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The discrete time analysis of the phase detector linear range extension in the first and the second order sub sampling phase-locked loop (SSPLL) is presented. The aim is to understand how much the stability and the pull-in range are affected by the linear ...

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

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An a posteriori error estimate is derived for the approximation of the transport equation with a time dependent transport velocity. Continuous, piecewise linear, anisotropic finite elements are used for space discretization, the Crank-Nicolson scheme schem ...

This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...

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We examine the almost-sure asymptotics of the solution to the stochastic heat equation driven by a Levy space-time white noise. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short tim ...

We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the mic ...

Analytical solutions to problems of solids mechanics are useful to test the accuracy and the precision of the numerical approaches. Problems such as shear locking or boundary layer can be better understood with the help of analytical solutions. However, it ...

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

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Discrete Time Analysis of Phase Detector Linear Range Extension in Sub-Sampling PLL

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

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Sub-nanosecond Optical Switching Using Chip-Based Soliton Microcombs

An adaptive algorithm for the transport equation with time dependent velocity

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Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems

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