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ABSTRACT
The faddeev leverrier' s algorithm is presented for finding real eigenvalues of any desired real matrices. The method features accuracy and simplicity. In contrast to. many previous techniques which merely afford one specific eigenvalue of a matrix, the method has the potential to provide all real eigenvalues. Also, the method does not require any initial guesses in its starting point unlike most of iterative techniques.
The Gershgorin circle theorem is a well-known and efficient method for bounding the eigenvalues of a matrix in terms of it entries. Furthermore, square matrices are often characterized by their eigenvalues, so we would like to be able to produce the eigenvalues for any square matrix. Co-factor expansion is an algorithm used to produce what is known as the characteristics polynomial of a matrix A, the roots of which are the eigenvalues of A. However, the algorithm for co-factor expansion is computationally intensive and as the output is an nth degree polynomial, we do not have any guaranteed method to find the roots for large matrices.
