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<p>Banded matrices are a critical class of matrices in numerical analysis when dealing with large-scale computational problems. This paper considers the inverses of generalized banded Toeplitz matrices with <i>l</i> sub-bands and <i>u</i> super-bands paralleling to the main diagonal, each located at a distance that is a multiple of <i>k</i> from the main diagonal. The focus is on utilizing the tensor product to establish a connection between the inverses of generalized banded Toeplitz matrices and those of general banded Toeplitz matrices with lower-order. Moreover, the explicit inverses of <i>k</i>-tridiagonal Toeplitz matrices and generalized pentadiagonal Toeplitz matrices are provided. Numerical experiments are provided to demonstrate the accuracy and efficiency of our proposed algorithms.</p>

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Tensor product factorization-based numerical algorithms for the inverses of generalized banded Toeplitz matrices

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Xin Fan,
  • Ji-Teng Jia

摘要

Banded matrices are a critical class of matrices in numerical analysis when dealing with large-scale computational problems. This paper considers the inverses of generalized banded Toeplitz matrices with l sub-bands and u super-bands paralleling to the main diagonal, each located at a distance that is a multiple of k from the main diagonal. The focus is on utilizing the tensor product to establish a connection between the inverses of generalized banded Toeplitz matrices and those of general banded Toeplitz matrices with lower-order. Moreover, the explicit inverses of k-tridiagonal Toeplitz matrices and generalized pentadiagonal Toeplitz matrices are provided. Numerical experiments are provided to demonstrate the accuracy and efficiency of our proposed algorithms.