Spline interpolation method in geometric (multiplicative) numerical analysis

In this thesis, firstly, the basic definitions and concepts of geometric analysis, which is one of the non-Newtonian analyses, are given. Then, the geometric derivatives of a geometric function at a point are calculated successively with classical derivatives. In addition, the geometrical derivatives at a point were calculated with the help of the Faà di Bruno formula with classical derivatives. The main subject of the thesis is the geometric spline interpolation method for geometric numerical analysis. Zero-order geometric spline interpolation, linear geometric spline interpolation, cubic geometric spline interpolation are introduced, respectively. In addition, the existence and uniqueness of the solution of the natural cubic geometric spline interpolation problem and the solution method are examined. Finally, an application of cubic geometric spline interpolation is given. The existence and uniqueness of the solution of the problem given in the application and the solution method are examined.