Recent Advancements in D-TTIT

|A brief history of the development of the Discrete Taylor Transform and Inverse Transform (D-TTIT) is followed by new insights which are encapsulated in three Theorems. In one dimension (1D) the required inverses of the matrices can be calculated simply-by-inspection. It is shown that this enabling property remains valid in 2D and 3D versions of D-TTIT, by utilizing matrix tensor products, which ``naturally'' arise in the formulation. Application areas include finite difference method, optimization, and where high-order difference formulae are needed on uniform or nonuniform grids.