Bounds for sine and cosine via eigenvalue estimation

Pentti Haukkanen; Mika Mattila; Jorma K. Merikoski; Alexander Kovacec

Special Matrices (2014)

  • Volume: 2, Issue: 1, page 19-29, electronic only
  • ISSN: 2300-7451

Abstract

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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.

How to cite

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Pentti Haukkanen, et al. "Bounds for sine and cosine via eigenvalue estimation." Special Matrices 2.1 (2014): 19-29, electronic only. <http://eudml.org/doc/267042>.

@article{PenttiHaukkanen2014,
abstract = {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.},
author = {Pentti Haukkanen, Mika Mattila, Jorma K. Merikoski, Alexander Kovacec},
journal = {Special Matrices},
keywords = {eigenvalue bounds; trigonometric inequalities},
language = {eng},
number = {1},
pages = {19-29, electronic only},
title = {Bounds for sine and cosine via eigenvalue estimation},
url = {http://eudml.org/doc/267042},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Pentti Haukkanen
AU - Mika Mattila
AU - Jorma K. Merikoski
AU - Alexander Kovacec
TI - Bounds for sine and cosine via eigenvalue estimation
JO - Special Matrices
PY - 2014
VL - 2
IS - 1
SP - 19
EP - 29, electronic only
AB - 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.
LA - eng
KW - eigenvalue bounds; trigonometric inequalities
UR - http://eudml.org/doc/267042
ER -

References

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