Some Research For Inverse Singular Value Problems Of Matrix

The inverse singular value problem is, in a constrained matrix set, finding the matrix such that partial singular values, left and right singular vectors are given. This problem is one of the topics of very active research in inverse problems with spectral constraint, and those has been widely used in principal component analysis, structural design, circuit theory, vibration theory, exploration and remote sensing, biology, mechanics, molecular spectroscopy, and so on. This thesis mainly studies following problems. By using the theory of Moore-Penrose generalized inverse, the characteristics of the singular values and singular vectors, the necessary and sufficient conditions for the existence of and the expression for the Problem 2 are derived. The thesis further study this problem with submatrics constraint which is to find the solution set of A such that two submatrics of A are given. The necessary and sufficient conditions for the existence of and the expression for the 3 are also obtained. By using the method of SVD and the ideal of matrix equation, the expression of 4 are given, the numerical methods and examples are also reported to illustrate the results.