2

2

9999520

Transformations between Bivariate Polynomial Bases

It is well known, that any interpolating polynomial p (x, y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y, has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of this short note is twofold : a) to present transformations between the coordinates of the polynomial p (x, y) in the aforementioned basis and b) to present transformations between these bases.

Bivariate interpolation polynomial, Polynomial basis,
Transformations.

1

10008128

A Parallel Implementation of k-Means in MATLAB

The aim of this work is the parallel implementation
of k-means in MATLAB, in order to reduce the execution time.
Specifically, a new function in MATLAB for serial k-means algorithm
is developed, which meets all the requirements for the conversion to a
function in MATLAB with parallel computations. Additionally, two
different variants for the definition of initial values are presented.
In the sequel, the parallel approach is presented. Finally, the
performance tests for the computation times respect to the numbers
of features and classes are illustrated.

K-means algorithm, clustering, parallel computations,
MATLAB.