Local Splines and the Least Squares Method

Abstract

The least squares method is widely used in processing quantitative results of natural science experiments, technical data, astronomical and geodetic observations and measurements. This paper proposes the construction of a modified least squares method based on the use of basis splines of a non-zero level. This modification allows us to obtain a continuously differentiable (required number of times) solution to the problem. The resulting solution is convenient to use to further solve other related problems. The construction of a continuously differentiable solution and a twice continuously differentiable solution is considered in more detail. These solutions are constructed based on the use of basis Hermitian splines of the fourth and sixth orders of approximation. The numerical results are presented for processing inaccurately specified experimental data, as well as for smoothing curves.