$B$-splines of high powers

The simple explicite expression was deduced for $B$-splines of arbitrary power on non-equidistant grid. The scalar productions of these splines were found up to the 7th power for equidistant grid. The algorithm of least square approximation of functions by such splines was developed. The universal test was proposed for checking different classes of algorithms. Numerical calculations on this test showed the algorithm was well posed and provided a high accuracy.