$$\mathcal O(n)$$O(n) working precision inverses for symmetric tridiagonal Toeplitz matrices with $$\mathcal O(1)$$O(1) floating point calculations

@article{Radons2018mathcalOW,
  title={\$\$\mathcal O(n)\$\$O(n) working precision inverses for symmetric tridiagonal Toeplitz matrices with \$\$\mathcal O(1)\$\$O(1) floating point calculations},
  author={Manuel Radons},
  journal={Optimization Letters},
  year={2018},
  volume={12},
  pages={425-434}
}
  • Manuel Radons
  • Published 27 November 2016
  • Mathematics
  • Optimization Letters
A well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal a on the diagonal and b on the extra diagonals ($$a, b\in \mathbb R$$a,b∈R). The inverses of such matrices are dense and there exist well known explicit formulas by which they can be calculated in $$\mathcal O(n^2)$$O(n2). In this note we present a simplification of the problem that has proven to be rather useful in everyday practice: If $$\vert a\vert > 2\vert b… 
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