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Bounds for sine and cosine via eigenvalue estimation

Pentti Haukkanen, Mika Mattila, Jorma K. Merikoski, Alexander Kovacec (2014)

Special Matrices

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...

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