Seven-diagonal run-through method for solving B-spline approximation problems

The B-spline approximation problem comes down to solving a system of linear equations with a symmetric coefficient matrix, which enables using the Cholesky method. This matrix is also a band one. If the degree of the splines is three (the most common case), the band width is seven. To solve systems with the said matrices, the Thomas algorithm is used. This is the name by which the method is known for a tridiagonal band. In this paper, a seven-diagonal version is investigated, and recurrence formulas are obtained. They are tested with the problem of smoothing altitude measurements using satellite geolocation. Compared to the Cholesky scheme, the technique is applicable to uncertain and asymmetric matrices and is more efficient in terms of computation speed and computer memory consumption. The results of numerical studies of the proposed scheme’s stability for ill-conditioned problems are presented