On the Least Squares Solution of Inverse Eigenvalue Problems

An inverse eigenvalue problem where a matrix is to be constructed from some or all of its eigenvalues may not have a real valued solution at all An approximate solution in the sense of least squares is sometimes desirable Two types of least squares problems are formulated and explored in this paper In spite of their di erent appearance the two problems are shown to be equivalent Thus one new numerical method modi ed from the conventional alternating projection method is proposed The method converges linearly and globally and can be used to generate good starting values for other faster but more expensive and locally convergent methods The idea can be applied to multiplicative inverse eigenvalue problems for the purpose of preconditioning Numerical examples are presented