Real Symmetric Quadratic Model Updating That Preserves Positive Definiteness and No Spill-over

Updating a model framed as a real symmetric quadratic eigenvalue problem to match observed spectral information has been a powerful tool for practitioners in different discipline areas. It is often desirable in updating to match only the part of newly measured data without tampering with the other part of unmeasured and often unknown eigenstructure inhering in the original model. Such an updating, known as no spill-over, has been a critical yet challenging task in practice. Only recently, a mathematical theory on updating with no spill-over has begun to be understood. In applications, however, often there is the additional requisite of maintaining positive definiteness in the coefficient matrices. Toward that need, this paper advances one step forward by preserving both no spill-over and positive definiteness of the mass and the stiffness matrices. This investigation establishes some necessary and sufficient solvability conditions for this open problem. AMS subject classifications. 65F18, 15A22, 93B55