A Low-Rank Matrix Approach to Compute Polynomial Approximations of Smooth Two-Dimensional Functions

• DOI: 10.1007/s11786-024-00581-2
• Publication Date: 2024-05-28T09:02:06Z
• Authors: Nilson J. Lima; José A. O. Matos; Paulo B. Vasconcelos
• Keywords: Low-rank approximation; Univariate; Rank (graph theory); Matrix (chemical analysis); Representation; Singular value

Abstract Polynomial approximation of smooth functions is becoming increasingly important in fields like numerical analysis and scientific computing. These approximations are vital models that rely on spectral methods. To reduce the memory costs for large dimensional problems, various methods to provide data-sparse representations have been proposed, including based singular value decomposition, adaptive cross approximation, matrices with hierarchical low-rank structures, mention a few. This work presents implementation details polynomial univariate through class, bivariate by matrix representation via class. approaches explained within , mathematical software library solving integro-differential problems Tau method.