Bounds for sine and cosine via eigenvalue estimation

• Autorzy: Pentti Haukkanen , Mika Mattila , Jorma K. Merikoski , Alexander Kovacec
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

eigenvalue bounds; trigonometric inequalities

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

wydano

2014-01-01

otrzymano

2013-10-04

zaakceptowano

2014-03-02

online

2014-04-09

Twórcy

autor

Pentti Haukkanen

• School of Information Sciences, FI-33014 University of Tampere, Finland

autor

Mika Mattila

• School of Information Sciences, FI-33014 University of Tampere, Finland

autor

Jorma K. Merikoski

• School of Information Sciences, FI-33014 University of Tampere, Finland

autor

Alexander Kovacec

• Department of Mathematics, University of Coimbra EC Santa Cruz, 3001-501 Coimbra, Portugal

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Identyfikatory

DOI

10.2478/spma-2014-0003