Solidification and Further Refinements

Summary

This chapter introduces matrix tensor product in Discrete Taylor Transform and Inverse Transform (D‐TTIT). The proposed style of numbering the grid points and the particular manner (y, x) their coordinates have been referenced have significant implications in designing the algorithms. It turns out that the desired inverses of the matrices of arbitrary finite dimension can be obtained simply‐by‐inspection. The successive elimination and back‐substitution processes involved in finding the inverses convey an astonishing insight into the D‐TTIT algorithm. The chapter illustrates the alternative procedure for the construction of difference operators based on the theory of frames. The involvement of matrix tensor products enables one to reduce the analysis of higher dimensional multivariate functions to the tensor product of one‐dimensional analysis. D‐TTIT permits the calculation of the mixed difference formulas at every grid point in the cluster.