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Area of Science:

  • Computational physics
  • Applied mathematics

Background:

  • Multivariate functions are essential in science but pose computational challenges regarding accuracy and memory.
  • Existing methods like quantics representation and tensor cross interpolation (TCI) offer partial solutions.

Purpose of the Study:

  • To present a novel computational strategy, quantics TCI, that integrates the strengths of quantics representation and TCI.
  • To demonstrate the efficacy of quantics TCI in a practical scientific application.

Main Methods:

  • The quantics representation encodes functions as multi-index tensors, using binary representations of variables.
  • Tensor cross interpolation (TCI) provides a method for parsimonious tensor approximation.
  • The proposed quantics TCI strategy combines these two techniques.

Main Results:

  • Quantics TCI successfully merges the benefits of quantics representation and TCI.
  • The method is demonstrated to be effective for computing Brillouin zone integrals in condensed matter physics.

Conclusions:

  • Quantics TCI offers a powerful new tool for the accurate and memory-efficient computation of multivariate functions.
  • This method has significant potential for applications in various scientific domains, including condensed matter physics.