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The local evaluation of the derivative of a determinant. (English) Zbl 0593.65028
The nonlinear lambda matrix problem is studied. When computing eigenvalues (points for which the matrix is singular), it is suggested that a Newton method finding the zeros of the determinant is used. It is described how to find values of the derivative of the determinant by means of diagonalization of the constant term in a Taylor series expansion of the $\lambda$ matrix.
Reviewer: A.Ruhe
65F40Determinants (numerical linear algebra)
65H17Eigenvalue and bifurcation problems of nonlinear algebraic equations (numerical methods)
15A54Matrices over function rings
65F15Eigenvalues, eigenvectors (numerical linear algebra)
Full Text: DOI
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