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Ullah, Malik, Alqarni, Abdulaziz, Alshomrani, Ali, Almuzaini, Mohammed, Asma, Mir. (1405). A Rapidly Convergent Iteration Scheme for Computing the Matrix Sign Function of Invertible Matrices. سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2025.67379.3203
Malik Zaka Ullah; Abdulaziz Saeed Alqarni; Ali Saleh Alshomrani; Mohammed Almuzaini; Mir Asma. "A Rapidly Convergent Iteration Scheme for Computing the Matrix Sign Function of Invertible Matrices". سامانه مدیریت نشریات علمی, , , 1405, -. doi: 10.22034/cmde.2025.67379.3203
Ullah, Malik, Alqarni, Abdulaziz, Alshomrani, Ali, Almuzaini, Mohammed, Asma, Mir. (1405). 'A Rapidly Convergent Iteration Scheme for Computing the Matrix Sign Function of Invertible Matrices', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2025.67379.3203
Ullah, Malik, Alqarni, Abdulaziz, Alshomrani, Ali, Almuzaini, Mohammed, Asma, Mir. A Rapidly Convergent Iteration Scheme for Computing the Matrix Sign Function of Invertible Matrices. سامانه مدیریت نشریات علمی, 1405; (): -. doi: 10.22034/cmde.2025.67379.3203

A Rapidly Convergent Iteration Scheme for Computing the Matrix Sign Function of Invertible Matrices

Computational Methods for Differential Equations
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 فروردین 1405    اصل مقاله (1.32 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.67379.3203
نویسندگان
Malik Zaka Ullah* 1؛ Abdulaziz Saeed Alqarni1؛ Ali Saleh Alshomrani1؛ Mohammed Almuzaini2؛ Mir Asma3
1Mathematical Modelling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia.
2Department of Mathematics, Jamoum University College, Umm Al-Qura University, Makkah, 25375, Saudi Arabia.
3Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, Tamil Nadu, India.
چکیده
This paper presents a novel 6th-rate multi-step iteration method to calculate the matrix sign function of an invertible matrix. The proposed scheme is constructed using rational approximations and carefully designed weight functions, leading to enhanced computational efficiency and high accuracy. A detailed convergence analysis is provided, including the derivation of an explicit error expression that rigorously establishes the method's sixth-order convergence rate. Additionally, we generalize the approach to matrix iteration frameworks, demonstrating that the eigenvalues of the generated iterates asymptotically converge to their theoretical limits. Numerical tests are conducted to validate the analytical findings and illustrate the superior performance of the presented method compared to existing techniques.
کلیدواژه‌ها
matrix function؛ eigenvalues؛ nonsingular؛ higher order؛ iteration solver
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