Computation of Partial Derivative of Matrix Determinant Arises in Multiparameter Eigenvalue Problems | Chapter 09 | Theory and Applications of Mathematical Science Vol. 1
This chapter considers an iterative
scheme based on Newton’s method to find the solution of eigenvalues of Linear
Multiparameter Matrix Eigenvalue Problems(LMEP). This chapter is also intended
to review some iterative algorithms for computation of partial derivatives of
matrix determinant involved in Newton’s Method. First algorithm is based on
standard Jacobi formula and second one is based on LU-decomposition Method
together with an algorithm to compute directly the entries of the matrices
involved in decomposition. Finally, an implicit determinant method is used for
the computation of the partial derivatives of matrix determinant. Although the
algorithms can be used to find the approximate eigenvalues of LMEPs, but the
numerical works are performed by considering three-parameter case for better
convenience and to relax computational cost and time. Numerical example is
presented to test the efficiency of each iterative algorithms. Errors in
computed eigenvalues are also compared with exact eigenvalues evaluated by
Δ-Method, adopted by Atkinson.
Author(s) Details
Niranjan Bora
Department of Mathematics,
Dibrugarh University Institute of Engineering and Technology (DUIET),
Dibrugarh, 786004, Assam, India.
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