Gradient flow methods for matrix completion with prescribed eigenvalues.
Matrix completion with prescribed eigenvalues is a special type of inverse eigenvalue problem which is a challenging problem both theoretically and computationally. In the present paper, the completion problem is recast as one of minimizing the distance between the isospectral matrices with prescribed eigenvalues and the affined matrices with prescribed entries. In the first part, the authors have chronicled some major developments on this subject in the literature. In the second part, they have proposed a dynamical system of which the trajectory allows one to complete the construction of a matrix numerically even under the situation when no existence theory is available at all. In the third part, numerical experiments seem to suggest that the idea of gradient flow approach can serve as a reasonable means to tackle the most general inverse eigenvalue problems with prescribed entries where the prescribed entries are at arbitrary locations with arbitrary cardinalities.
scientific article; zbMATH DE number 2056679
scientific article