  In this note, we briefly present a generalized tensor CUR (GTCUR)
approximation for tensor pairs (X,Y) and tensor triplets (X,Y,Z) based on the
tubal product (t-product). We use the tensor Discrete Empirical Interpolation
Method (TDEIM) to do these extensions. We show how the TDEIM can be utilized to
generalize the classical tensor CUR (TCUR) approximation, which acts only on a
single tensor, to jointly compute the TCUR of two and three tensors. This
approach can be used to sample relevant lateral/horizontal slices of one data
tensor relative to one or two other data tensors. For some special cases, the
Generalized TCUR (GTCUR) approximation is reduced to the classical TCUR for
both tensor pairs and tensor triplets in a similar fashion as shown for the
matrices.
