Modern techniques for fitting generalized additive models mostly rely on basis expansions of covariates using a large number of basis functions and penalized estimation of parameters. We exemplarily use a mixed model approach to fit a model for children’s lung function that allows for non-linear influence of several covariates available in a substantial data set. While the resulting model is ex...

We first review B-splines and splines constructed using B-splines as the basis functions.

Adaptive B-spline Knots Selection Using Multi-Resolution Basis Set Yuan Yuan, Nan Chen, Shiyu Zhou a Department of Industrial and Systems Engineering, the University of Wisconsin – Madison b Department of Industrial & Systems Engineering, National University of Singapore c Corresponding author. Email: [email protected] ABSTRACT B-splines are commonly used in the Computer Aided Design (CAD) an...

We investigated the benefit of incorporating a negativity penalty into a least-squares criterion used to reconstruct 3-D radiotracer distributions in cardiac SPECT studies. B-spline spatial basis functions were used to provide a continuous model for the 3-D tracer distribution. Spline coefficients that tended to have negative values were identified and were constrained to stay near zero with us...

We interpret a type of fuzzy controller as an inter polator of B spline hypersurfaces B spline basis func tions of di erent orders are regarded as a class of mem bership functions MFs with some special properties These properties lead to several interesting conclusions about fuzzy controllers if such membership functions are employed to specify the linguistic terms of the input variables We sho...

In this paper we present an approach to designing a novel type of fuzzy controller B spline basis functions are used for input variables and fuzzy singletons for output variables to specify linguistic terms Product is chosen as the fuzzy conjunction and centroid as the defuzzi ca tion method By appropriately designing the rule base a fuzzy controller can be interpreted as a B spline interpolato...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...

As a rule, an energy method is widely adopted for b-spline curve smoothing, but this method has the disadvantages such as massive calculation, computation complexity and low efficiency. Compared with the energy method, multi-resolution smoothing approaches nicely overcome these obstacles. Presently, some researches have been conducted on multi-resolution smoothing, but these efforts mainly aime...

The layout of the survey is as follows. After a short discussion of cardinal B-splines, i.e., of B-splines on a uniform knot sequence, in Section 2, B-splines for an arbitrary knot sequence are introduced in Section 3 and shown to be a basis for certain spaces of piecewise polynomial functions. Various simple properties of B-splines are listed in Section 4, and the relationship between a spline...

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show t...