Septic-convolution Kernel - Comparative Analysis of the Interpolation Error

Abstract

The first part of the paper describes the septic-convolution (QC) interpolation kernel. The SC kernel consists of seventh-order polynomials and approximates the ideal sinc function in the interval [−4; 4]. The second part of the paper presents the results of the Experiment, which was realized with the aim of determining the interpolation error, MSE, when interpolating with the interpolation SC kernel. In addition, a comparative analysis with interpolation error, which occurred during interpolation with an interpolation fifth-order polynomial kernel (QC kernel), was performed. After that, the analysis of the values of the kernel parameters, α, determined theoretically and experimentally, is presented. Deviations of the theoretical values, in relation to experimental ones, were analyzed over statistical parameters (µ, σ2). Finally, the efficiency of the algorithm for estimating the theoretical values of the kernel parameters, using parameters Accuracy and Precision, was determined. Experimental results are shown in tables and by graphs.