The ideas of tensor decomposition can be further integrated with the Loewner framework to achieve even more efficient multivariate function approximation. By leveraging tensor decomposition techniques such as Canonical Polyadic Decomposition (CPD), Tucker Decomposition, or Tensor Train Decomposition, the high-dimensional data structures can be efficiently represented and manipulated. This integration can help in reducing the computational complexity of handling large-scale multivariate functions, making the approximation process more scalable and efficient. Additionally, tensor decomposition can provide insights into the underlying structure of the multivariate functions, leading to improved modeling and analysis capabilities.