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https://hdl.handle.net/10316/109685
Title: | Bounds for sine and cosine via eigenvalue estimation | Authors: | Haukkanen, Pentti Mattila, Mika Merikoski, Jorma K. Kovacec, Alexander |
Keywords: | eigenvalue bounds; trigonometric inequalities | Issue Date: | 2014 | Publisher: | Walter de Gruyter | Serial title, monograph or event: | Special Matrices | Volume: | 2 | Issue: | 1 | Abstract: | De ne n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the rst 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 rst super- and subdiagonal are minus one. Then, denoting by (·) the largest eigenvalue, (T) = 2 cos n + 1 , (S−1) = 1 4 cos2 n 2n+1 . 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. | URI: | https://hdl.handle.net/10316/109685 | ISSN: | 2300-7451 | DOI: | 10.2478/spma-2014-0003 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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