陳界山Jein-Shan Chen余政和Cheng-He Yu2019-09-052015-07-292019-09-052015http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22G060240031S%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101534無中文摘要The system of absolute value equations Ax + B|x| = b, denoted by AVEs, is a non-differentiable NP-hard problem, where A,B are arbitrary given n × n real matrices and b is arbitrary given n-dimensional vector. In this paper, we study four new smoothing functions and propose a smoothing-type algorithm to solve AVEs. With the assumption that the minimal singular value of the matrix A being strictly greater than the maximal singular value of the matrix B, we prove that the algorithm is globally and locally quadratically convergent with the four smooth equations.平滑函數奇異值收斂Smoothing functionsingular valueconvergence