Computing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
1 - Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.
کلید واژه: Stability, Sign function, HPD, Convergence, Iterative methods,
چکیده مقاله :
A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix square root. Finally, several experiments are collected.
در این مقاله، یک روش تکراری کارا برای محاسبه علامت یک ماتریس که هیچ مقدار ویژه ی موهومی ندارد ارائه می شود. سپس با استفاده از یک همسانی شناخته شده در تئوری عملکرد ماتریس ها، یک الگوریتم برای محاسبه میانگین هندسی از دو ماتریس هرمیتی معین مثبت بدست می آید. علاوه بر این یک الگوریتم کارامد دیگر برای این هدف ارائه میشود که وابسته به جذر ماتریس نباشد. وسرانجام چند آزمایش هم برای نمایش کاربرد آن انجام خواهد شد.
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