Define n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the first super- and subdiagonal are one. The entries of the main diagonal of S are two except the (n, n) entry one, and those of the first super- and subdiagonal are minus one. Then, denoting by λ(·) the largest eigenvalue, [...] Using certain lower bounds for the largest eigenvalue, we provide lower bounds for these expressions and, further, lower bounds for sin x and cos x on certain intervals. Also upper bounds can be obtained in this way.
@article{bwmeta1.element.doi-10_2478_spma-2014-0003,
author = {Pentti Haukkanen and Mika Mattila and Jorma K. Merikoski and Alexander Kovacec},
title = {Bounds for sine and cosine via eigenvalue estimation},
journal = {Special Matrices},
volume = {2},
year = {2014},
zbl = {1291.15049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0003}
}
Pentti Haukkanen; Mika Mattila; Jorma K. Merikoski; Alexander Kovacec. Bounds for sine and cosine via eigenvalue estimation. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0003/
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