Newton Iterative Methods for a Class of Quadratic Matrix Equations and Its Convergence
Quadratic matrix equation is an important kind of equations in scientific and engi-neering computations,and it is a meaningful work to explore some effective numerical methods.A special class of quadratic matrix equations derived from quasi-birth-death processes is stud-ied.The quasi-birth-death process has important applications in many fields such as stock price simulation,inventory control,queuing theory,etc.Under the assumption that the minimum non-negative solution exists and is unique,the Newton iteration method is proposed and its convergence is proved.When the initial matrix is zero matrix,the matrix sequence generated by Newton iteration method converges to the unique minimum non-negative solution.Finally,numerical examples are used to verify the effectiveness and feasibility of the algorithm.
quadratic matrix equationthe process of quasi-birth and deathminimum non-negative solutionNewton iterationconvergence
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