Solving constrained quadratic inverse eigenvalue problem via conjugate direction method

Inverse eigenvalue problems are among the most important problems in numerical linear algebra. This paper is concerned with the problem of designing an iterative method for a quadratic inverse eigenvalue problem of the form MX Lambda(2) GX Lambda + KX = 0 where M, G and K should be partially doubly symmetric under a prescribed submatrix constraint. This kind of quadratic inverse eigenvalue problem includes the classical and generalized inverse eigenvalue problems as special cases. We propose the conjugate direction (CD) method for computing the least Frobenius norm solutions of this constrained quadratic inverse eigenvalue problem in a finite number of steps in the absence of round-off errors. The CD method can automatically determine the solvability of this problem. Finally, the overall performance and efficiency of the CD method for computing approximate solutions of the problem are discussed. (C) 2018 Elsevier Ltd. All rights reserved.