2017/10/17 by Jonathan D. Hauenstein, Hauenstein, Jonathan D., Margaret H. Regan +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1710.06362
openalex publication_date 2017/10/17 · openalex created_date 2022/08/07 · openalex updated_date 2026/07/28
Three aspects of applying homotopy continuation, which is commonly used to\nsolve parameterized systems of polynomial equations, are investigated. First,\nfor parameterized systems which are homogeneous, we investigate options for\nperforming computations on an adaptively chosen affine coordinate patch.\nSecond, for parameterized systems which are overdetermined, we investigate\noptions for adaptively selecting a well-constrained subsystem to restore\nnumerical stability. Finally, since one is typically interested in only\ncomputing real solutions for parameterized problems which arise from\napplications, we investigate a scheme for heuristically identifying solution\npaths which appear to be ending at nonreal solutions and truncating them. We\ndemonstrate these three aspects on two problems arising in computer vision.\n