Details

Autor(en) / Beteiligte

• Seo, Sang-Hyup
• Seo, Jong-Hyun
• Kim, Hyun-Min

Titel

NEWTON'S METHOD FOR SOLVING A QUADRATIC MATRIX EQUATION WITH SPECIAL COEFFICIENT MATRICES

Ist Teil von

• 호남수학학술지, 2013, 35(3), , pp.417-433

Ort / Verlag

호남수학회

Erscheinungsjahr

2013

Link zum Volltext

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• We consider the iterative solution of a quadratic matrixequation with special coefficient matrices which arises in the quasibirthand death problem. In this paper, we show that the elementwiseminimal positive solvent of the quadratic matrix equationscan be obtained using Newton’s method if there exists a positivesolvent and the convergence rate of the Newton iteration is quadraticif the Fr´echet derivative at the elementwise minimal positivesolvent is nonsingular. Although the Fr´echet derivative is singular,the convergence rate is at least linear. Numerical experiments ofthe convergence rate are given. KCI Citation Count: 0