Improved Newton's method with exact line searches to solve quadratic matrix equation
A method for solving the matrix equation \(AX^2 + BX + C=0\) is given. There are two main contributions: First, the incorporation of Newton's method with exact new line searches is to reduce the computational cost, and second, the use of the technique of \textit{V. E. Shamanskij} [Ukrain Math. Z. 19, No.~1, 133--138 (1967; Zbl 0176.13802)] to get a faster rate of convergence. Theoretical and computational results are presented to show the efficiency of the proposed method.
scientific article; zbMATH DE number 5368395