Based on various matrix decompositions, we compare different techniques
for solving the inverse quadratic eigenvalue problem, where n × n real symmetric matrices M, C and K are constructed so that the quadratic pencil Q(λ) = λ2M + λC + K
yields good approximations for the given k eigenpairs. We discuss the case where M is
positive definite for 1 ≤ k ≤ n, and a general solution to this problem for n+1 ≤ k ≤ 2n.
The efficiency of our methods is illustrated by some numerical experiments.