Using Smolyak’s construction [5], we derive a new algorithm for approximating multivariate functions over bounded or unbounded regions in R with the error measured in a weighted L1-norm. We provide upper bounds for the algorithm’s cost and error for a class of functions whose mixed first order partial derivatives are bounded in L1-norm. In particular, we prove that the error and the cost (measu...

Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to sequence functions and modify norm in its internal optimization problem H−s norm, some positive integer s, bias it towards low-frequency spectral content residual. We analyze by quantifying improvement over Picard iteration. find that based on H−2 well-suited solve...

Sprint interval training (SIT) is an efficient intervention capable of improving aerobic capacity and exercise performance. This experiment aimed to determine differences in training adaptations and the inflammatory responses following 2 weeks of SIT (30 s maximal work, 4 min recovery; 4-7 repetitions) performed in normoxia or hypoxia. Forty-two untrained participants [(mean ± SD), age 21 ±1 ye...

In this work, we introduce a new 2-norm generated by bounded linear functionals on normed space X with dimension dim(X) ? 2, and investigate its relationship the G?hler?s [Lineare 2-normierte R?ume, Math. Nachr.]. We also derive norm to explore relation usual X.

This study examines the issue of norm construction in al-Ghazālī’s thought focusing on grounds advanced to support his radical infallibilist position. To fulfill such end, al-Ghazālī, I explain, relies two types arguments, first one relates presumptive nature legal texts order highlight their fundamental indeterminacy and second links interpreter show impossibility fall into error. buttress the...

In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in highfrequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L-norm. In particular, the error in the energy norm is shown to converge with the optimal order O(hmin...

We consider the problem of approximating a multiple-input multiple-output (MIMO) p×m rational transfer function H(s) of high degree by another p×m rational transfer function b H(s) of much smaller degree, so that the H2 norm of the approximation error is minimized. We characterize the stationary points of the H2 norm of the approximation error by tangential interpolation conditions and also ext...

For a set S of distinct points in the x-y plane and a 3-dimensional surface with the general quadratic equation f ey dx cxy by ax z + + + + + = 2 2 we study the problem of finding a locally optimal triangulation of S for the linear approximation of the surface under the Lp norm. We show that the Lp norm error is independent of the translation and rotation by 180 degrees of a single triangle in ...