Constructing a Matrix Mid-Point Iterative Method for Matrix Square Roots and Applications
نویسندگان
چکیده
In this paper, an improvement to the mid-point method is contributed for finding square root of a matrix as well its inverse. To aim, iteration scheme find function constructed, and error stability estimates are provided show theoretical rate convergence. Our higher-order can compete with existing iterative methods similar nature. This illustrated in numerical simulations various sizes.
منابع مشابه
ON CONEIGENVALUES OF A COMPLEX SQUARE MATRIX
In this paper, we show that a matrix A in Mn(C) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. And also show that if allconeigenvalues of conjugate-normal matrix A be real, then it is symmetric.
متن کاملConstructing and Validating a Q-Matrix for Cognitive Diagnostic Analysis of a Reading Comprehension Test Battery
Of paramount importance in the study of cognitive diagnostic assessment (CDA) is the absence of tests developed for small-scale diagnostic purposes. Currently, much of the research carried out has been mainly on large-scale tests, e.g., TOEFL, MELAB, IELTS, etc. Even so, formative language assessment with a focus on informing instruction and engaging in identification of student’s strengths and...
متن کاملNewton's Method for the Matrix Square Root*
One approach to computing a square root of a matrix A is to apply Newton's method to the quadratic matrix equation F( X) = X2 A =0. Two widely-quoted matrix square root iterations obtained by rewriting this Newton iteration are shown to have excellent mathematical convergence properties. However, by means of a perturbation analysis and supportive numerical examples, it is shown that these simpl...
متن کاملThe least-square bisymmetric solution to a quaternion matrix equation with applications
In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. As applications, we derive sufficient and necess...
متن کاملVerified Computation of Square Roots of a Matrix
We present methods to compute verified square roots of a square matrix A. Given an approximation X to the square root, obtained by a classical floating point algorithm, we use interval arithmetic to find an interval matrix which is guaranteed to contain the error of X. Our approach is based on the Krawczyk method which we modify in two different ways in such a manner that the computational comp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10132200