# Secular equation

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Related to Secular equation: Characteristic equation, Characteristic root
 (Astron.) the algebraic or numerical expression of the magnitude of the inequalities in a planet's motion that remain after the inequalities of a short period have been allowed for.

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
References in periodicals archive ?
By solving the secular equation (11a), we found eigenvalues [[??].sub.k] and eigenvectors [C.sup.(k).sub.nm], k = 1,2,3, ....
The numerical solution of the secular equation (H.2) gives the following set of roots:
In order to highlight it we must note that the main masses are the solution to the secular equation of the respective matrix, which can be written as [9]
The results depict the variation of Stoneley waves velocity and attenuation coefficient, Stoneley secular equation, Rayleigh secular equation, Rayleigh waves velocity and attenuation coefficient, Love waves velocity and attenuation coefficient, and Love secular equation in the context of four theories.
Equation (29) is surface waves secular equation of fiber-reinforced transversely isotropic thermoelastic half-space under a uniform homogeneous inviscid liquid layer.
The question of agreeing or disagreeing with his safe 'secular equation' of the two national parties lay beyond a 'true or false' type question asked on a high-school examination-question paper.
The propagation of surface (Rayleigh) waves over a rotating orthorhombic crystal was studied [10], in which the secular equation for the surface wave speed was found explicitly.
According to the Jacobi matrix [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] , it is easy to obtain the secular equation of (5):
Cybenko and Van Loan (Cybenko & Van Loan, 1986) presented an algorithm, which is a combination of bisection and Newton's method for the secular equation. This approach was improved considerably in (Mackens & Voss, 1997) and (Kostic & Voss, 2002) by replacing Newton's method by a more appropriate root finding methods for the secular equation.
Due to its special structure possessed by Toeplitz matrices we use the information we obtain from the appropriate matrix of a smaller size for calculating the value of the characteristic polynomial or the secular equation. Durbin's algorithm is used to solve Yule-Walker system:
Cybenko and Van Loan (Cybenko & Van Loan, 1986) presented an algorithm which is a combination of bisection and Newton's method for the secular equation. This approach was improved considerably in (Mackens & Voss 1997) and (Kostic & Voss, 2002) by replacing Newton's method by a more appropriate root finding methods for the secular equation.
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