2017/01/26 by Lixing Han, Han, Lixing
Mathematics · #65H10 #65H20 #Advanced Optimization Algorithms Research #Algebra over a field #Applied mathematics #Complementarity (molecular biology) #Convergence (economics) #FOS: Mathematics #Fractional Differential Equations Solutions #Homotopy #Homotopy analysis method #Invertible matrix #Mathematical analysis #Mathematics #Multilinear map #Numerical Analysis (math.NA) #Numerical analysis #Partial differential equation #Pure mathematics #Tensor (intrinsic definition) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1701.07536
openalex publication_date 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive solution to a multilinear system with a nonsingular M-tensor and a positive right side vector. We analyze the method and prove its convergence to the desired solution. We report some numerical results based on an implementation of the proposed method using a prediction-correction approach for path following.