# $$\mathcal O(n)$$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},
journal={Optimization Letters},
year={2018},
volume={12},
pages={425-434}
}
• 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…
1 Citations
Convergence results for some piecewise linear solvers
• Computer Science
Optimization Letters
• 2021
It is shown that the piecewise linear equation system, based on the jats:inline-formula, can be implemented as a discrete-time solution to the inequality problem.

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