Fast enclosure for solutions of Sylvester equations

作者：Miyajima Shinya^*

来源：Linear Algebra and Its Applications, 2013, 439(4): 856-878.

DOI：10.1016/j.laa.2012.07.001

• Numerical enclosure
• Sylvester equation
• Lyapunov equation

Fast algorithms for enclosing solutions of Sylvester equations AX + XB = C, A is an element of C-mxm, B is an element of C-nxn, X, C is an element of C-mxn are proposed. The results obtained by these algorithms are %26quot;verified%26quot; in the sense that all the possible rounding errors have been taken into account. For developing these algorithms, theories which directly supply error bounds for numerical solutions are established. The proposed algorithms require only O(m(3) + n(3)) operations if A and B are diagonalizable. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms.

• 出版日期2013-8-15