This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results the tracking iterate error (the limit supremum of norm difference between optimal solution iterates) gradient descent are derived. The then considers a general first-order framew...

In this paper, we further analyze, improve and develop the conservative fronttracking method developed in Mao(1995, SIAM. J. Numer. Anal., 32, 1677– 1703). The method in Mao(1995, SIAM. J. Numer. Anal., 32, 1677–1703) is only first-order accurate near the tracked discontinuities when applied to systems of conservation laws. This is because in the system case near tracked discontinuities there a...

Starting from the study of the Shepard nonlinear operator of max-prod type by Bede et al. 2006, 2008 , in the book by Gal 2008 , Open Problem 5.5.4, pages 324–326, the Bernstein max-prod-type operator is introduced and the question of the approximation order by this operator is raised. In recent paper, Bede and Gal by using a very complicated method to this open question an answer is given by o...

the purpose of this article is to use the classical sampling theorem, wks sampling theorem, to deriveapproximate values of the eigenvalues of the sturm-liouville problems with eigenparameter in the boundaryconditions. error analysis is used to give estimates of the associated error. higher order approximations are also drived, which lead to more complicated computations. we give some examples a...