In this paper, we propose and validate a computationally efficient non-iterative domain decomposition procedure for calculating bivariate cubic L1 smoothing splines. This domain decomposition procedure involves calculating local L1 smoothing splines individually on overlapping “extended subdomains” that cover the global domain and then creating the global L1 smoothing spline by patching togethe...

Pseudo-splines constitute a new class of refinable functions with B-splines, interpolatory refinable functions and refinable functions with orthonormal shifts as special examples. Pseudo-splines were first introduced by Daubechies, Han, Ron and Shen in [Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal. 14(1) (2003), 1–46] and Selenick in [Smooth wavelet tight fra...

This essay reviews those basic facts about (univariate) B-splines that are of interest in CAGD. The intent is to give a self-contained and complete development of the material in as simple and direct a way as possible. For this reason, the B-splines are defined via the recurrence relations, thus avoiding the discussion of divided differences which the traditional definition of a B-spline as a d...

the possibility of applying membrane distillation to support the fermentation process was investigated. the capillary polypropylene membranes were assembled in the membrane modules. the studies were carried out using the standard solutions containing the compounds frequently occurring in the broths such as ethanol, citric, acetic and lactic acids, glycerol and 1,3-propanediol. the performance o...

background: meniere’s disease (md) is a chronic illness defined as an idiopathic syndrome of endolymphatic hydrops. benign paroxysmal positional vertigo (bppv) is a balance disorder and can be the sequel of diverse inner ear impairments. objectives: the purpose of this study was to investigate the prevalence of bppv in md patients. materials and methods: all patients with definite or probable m...

The asymptotic behaviour of penalized spline estimators is studied in the univariate case. We use B -splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya-Watson kernel estimators with ‘equivalent’ kernels depending upon m. The ...