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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

MSC:

65F40 Numerical computation of determinants
65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
15A54 Matrices over function rings in one or more variables
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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