TY - JOUR
T1 - An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations
AU - Sogabe , T.
AU - Suzuki , A.
AU - Zhang , S.-L.
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 142
EP - 154
PY - 2020
DA - 2020/03
SN - 1
DO - http://doi.org/10.4208/csiam-am.2020-0008
UR - https://global-sci.org/intro/article_detail/csiam-am/16796.html
KW - Shifted linear systems, symmetric positive definite, the shifted conjugate gradient method, sphere constrained quadratic optimizations, Ye’s hybrid method.
AB - <p style="text-align: justify;">An implicit evaluation method of vector 2-norms is presented for function
evaluations arising from sphere constrained quadratic optimizations. The efficiency of
the method in terms of computational costs mainly comes from the well-known shifted
conjugate gradient method, and the robustness of the method comes from the fact that
it never suffers from cancellations when the coefficient matrix is symmetric positive
definite. Numerical experiments indicates that the method is promising for reducing
computational costs of Ye&#39;s hybrid method for solving sphere constrained quadratic
optimizations.</p>