Mahsa Bagheri, Faranges Kyanfar, Abbas Salemi, Azita Tajaddini
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A modified block Hessenberg method for low-rank tensor Sylvester equation
This work focuses on iteratively solving the tensor Sylvester equation with low-rank right-hand sides. To solve such equations, we first introduce a modified version of the block Hessenberg process so that approximation subspaces contain some extra block information obtained by multiplying the initial block by the inverse of each coefficient matrix of the tensor Sylvester equation. Then, we apply a Galerkin-like condition to transform the original tensor Sylvester equation into a low-dimensional tensor form. The reduced problem is then solved using a blocked recursive algorithm based on Schur decomposition. Moreover, we reveal how to stop the iterations without the need to compute the approximate solution by calculating the residual norm or an upper bound. Eventually, some numerical examples are given to assess the efficiency and robustness of the suggested method.
期刊介绍:
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.