New Algorithms For The Inverse Eigenvalue Problems IEP With Parameters And The Inverse Singular Value Problems ISVP With Parameters

Inverse eigenvalue(singular value)problem of matrices is one of the main topics of the numerical algebra,which has important applications in many fields.In this thesis,we study the numerical methods for a class of parameterized inverse eigenvalue problems(IEP)and parameterized inverse singular value problems(ISVP).For IEP,we first transform it into a problem of solving nonlinear equations,and then combine Ulm method for solving operator equations with the algorithm for IEP given in [Aishima K,A quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems,Linear Algebra Appl,2018,542:310-333],and construct a Ulm-type algorithm for solving IEP,it is proved that under the conditions that the given spectrum data are different from each other,the algorithm has the quadratic convergence in the sense of root convergence.The algorithm avoids the shortcomings of solving a system of linear equations in each iteration,therefore,it reduces the complexity and improves the stability of the algorithm.The numerical experiments show that the proposed algorithm is better than the existing algorithm when the matrix order is larger.For ISVP,a new method based on matrix equation with low computational complexity is constructed,under some conditions,we show that the given algorithm converges locally quadratically.The numerical experiments show that the proposed algorithm is more efficient than the existing algorithm.