Article ID: | iaor19951509 |
Country: | United States |
Volume: | 19 |
Issue: | 4 |
Start Page Number: | 815 |
End Page Number: | 830 |
Publication Date: | Nov 1994 |
Journal: | Mathematics of Operations Research |
Authors: | Wolkowicz Henry |
Keywords: | matrices |
Measures of deviation of a symmetric positive definite matrix from the identity are derived. They give rise to symmetric rank-one, SR1, type updates. The measures are motivated by considering the volume of the symmetric difference of the two ellipsoids, which arise from the current and updated quadratic models in quasi-Newton methods. The measure defined by the problem-maximize the determinant subject to a bound of 1 on the largest eigenvalue-yields the SR1 update. The measure