Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splinets -- splines through the Taylor expansion, their support sets and
  orthogonal bases   A new representation of splines that targets efficiency in the analysis of
functional data is implemented. The efficiency is achieved through two novel
features: using the recently introduced orthonormal spline bases, the so-called
{\it splinets} and accounting for the spline support sets in the proposed
spline object representation. The recently-introduced orthogonal splinets are
evaluated by {\it dyadic orthogonalization} of the $B$-splines. The package is
built around the {\it Splinets}-object that represents a collection of splines.
It treats splines as mathematical functions and contains information about the
support sets and the values of the derivatives at the knots that uniquely
define these functions. Algebra and calculus of splines utilize the Taylor
expansions at the knots within the support sets. Several orthonormalization
procedures of the $B$-splines are implemented including the recommended dyadic
method leading to the splinets. The method bases on a dyadic algorithm that can
be also viewed as the efficient method of diagonalizing a band matrix. The
locality of the $B$-splines in terms of the support sets is, to a great extend,
preserved in the corresponding splinet. This together with implemented
algorithms utilizing locality of the supports provides a valuable computational
tool for functional data analysis. The benefits are particularly evident when
the sparsity in the data plays an important role. Various diagnostic tools are
provided allowing to maintain the stability of the computations. Finally, the
projection operation to the space of splines is implemented that facilitates
functional data analysis. An example of a simple functional analysis of the
data using the tools in the package is presented. The functionality of the
package extends beyond the splines to piecewise polynomial functions, although
the splines are its focus.

31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
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The categories of this paper are: adap-org