Theoretical analysis and numerical solution to a vector equation $Ax-\|x\|_1x=b$ Article Swipe
Theoretical and computational properties of a vector equation $Ax-\|x\|_1x=b$ are investigated, where $A$ is an invertible $M$-matrix and $b$ is a nonnegative vector. Existence and uniqueness of a nonnegative solution is proved. Fixed-point iterations, including a relaxed fixed-point iteration and Newton iteration, are proposed and analyzed. A structure-preserving doubling algorithm is proved to be applicable in computing the required solution, the convergence is at least linear with rate 1/2. Numerical experiments are performed to demonstrate the effectiveness of the proposed algorithms.
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- http://arxiv.org/abs/2507.04971
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Theoretical analysis and numerical solution to a vector equation $Ax-\|x\|_1x=b$Work title
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2025Year of publication
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2025-07-07Full publication date if available
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Yiheng Wang, Gwi Soo Kim, Jie MengList of authors in order
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https://arxiv.org/abs/2507.04971Publisher landing page
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https://arxiv.org/pdf/2507.04971Direct link to full text PDF
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0Total citation count in OpenAlex
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