# 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

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topPentti 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 -

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