Noaman Salam Abdulkhaleq, Al-Mahdawi H K, Al-Nuaimi Bashar Talib, Sidikova A I
University of Diyala, Diyala 32001, Iraq.
Department of System Programming, South Ural State University, Chelyabinsk 454080, Russia.
MethodsX. 2023 May 7;10:102210. doi: 10.1016/j.mex.2023.102210. eCollection 2023.
In this work, we study the iterative method for solving linear operator equation of the first kind. We present a new version of method based on the applied the iterative performance on the modified Lavrentiev method. This method is used to resolve a linear operator problem of the first kind. The suggested iterative can used to compute approximate solutions with high quality than the (standard) modified Lavrentiev regularization method. We also compared the new iterative method (modified Lavrentiev) with Landweber iterative method. The numerical testing shows the efficiency of the new iterative method in its application to resolve the inverse heat equation when trying to find the boundary value function. •Studying of new iteration algorithm and mathematical experimentations show the efficiency of the new iteration method.•Iteration method is depended on decomposed the main linear operator by using polar decomposition in order to obtain unitary operator.•The new unitary operator increases the convergence of iteration.
在这项工作中，我们研究求解第一类线性算子方程的迭代方法。我们基于在修正的拉夫连季耶夫方法上应用迭代性能提出了一种新的方法版本。该方法用于解决第一类线性算子问题。所提出的迭代方法能够比（标准的）修正拉夫连季耶夫正则化方法更高效地计算高质量的近似解。我们还将新的迭代方法（修正的拉夫连季耶夫方法）与兰德韦伯迭代方法进行了比较。数值测试表明，在尝试求解逆热方程以找到边界值函数时，新的迭代方法在应用中具有高效性。•对新迭代算法的研究和数学实验表明了新迭代方法的有效性。•迭代方法依赖于通过极分解对主要线性算子进行分解以获得酉算子。•新的酉算子提高了迭代的收敛性。
