An alternating maximization method for approximating the hump of the matrix exponential

作者：Sadkane Miloud^*; Sidje Roger B

来源：BIT Numerical Mathematics, 2017, 57(3): 609-628.

DOI：10.1007/s10543-016-0644-7

• Hump of the matrix exponential
• Alternating maximization
• Stable matrix

Although the principle of alternating maximization is well known in the optimization literature, it has not been used before in the context of calculating the hump of the matrix exponential. We propose a method that applies alternating maximization in this particular context, and we show that it has a number of advantages over traditional Newton-like methods. We establish convergence results that fit this context with mild assumptions than would otherwise be the case in general optimization problems. We conduct numerical tests to complement the theory and they show convergence in just a few iterations.

• 出版日期2017-9