Greatest Common Factor Algorithm And Matrix Inverse Eigenvalue Problem,

The way to evaluate the greatest common factor of some polynomials is a algebra problem, which is also full of vigor in the practical application. In chapter one of this paper, the author introduces the typical way to evaluate the greatest common factor of some polynomials and some results that are studied by the scholars of the same trade. In the recent years, as the requirement of the practice, the studying to the inverse problems for matrices especially for the eigenvalue of matrices has become a subject that is very active in the calculation mathematics nowadays. In chapter one of this paper, the author sets forth the background and practice of this problem, give the mathematics model and introduces the achievements which are studied by the scholars of the same trade.In chapter two of this paper, firstly the author gives the matrix express for some polynomials, advances the new concept of the first and second oblique elementary operation of matrices. Then gives a new way to evaluate the greatest common factor of some polynomials. The author provides the theory proof and the example to themethod.In chapter three of this paper, the author studies the inverse problems for matrix eigenvalue. Based on the concept of secondary eigenvalue and secondary eigenvector, the author gives the model for the inverse problem of secondary eigenvalue of the matrix, discusses the inverse problems of secondary eigenvalue for anti-skew-symmetric matrices on a linear manifold. The necessary and sufficient conditions and expression of the solution of these problems is given. By using the secondary unit matrix, the inverse problem of secondary eigenvalue of anti-skew-symmetric is solved.In chapter four of this paper, based on the theory of chapter two, by applying the oblique elementary of matrix or the second oblique elementary of matrix, the algorithm for solving the greatest common factor is presented. Thus the solving of the greatest common factor becomes fast simple and practical. At last, a example about the practice of the algorithm is given.In chapter five of this paper, the author looks ahead his direction of the study work in the future.