Verified error bounds for singular solutions of nonlinear systems

• DOI: 10.1007/s11075-014-9948-3
• Publication Date: 2014-12-16T19:29:34Z
• Authors: Zhe Li; Haifeng Sang
• Keywords: Theory of computation; Singular solution; Rank (graph theory)

We discuss the verification for isolated singular solutions and non-isolated singular solutions with maximum rank deficiency of general nonlinear systems which have all the relevant partial derivatives. Using the border system technique, we present a deflation algorithm to compute verified error bound for such a singular solution of the given system or for a solution of a slight perturbed system, where the solution of the slight perturbed system is near the above singular solution of the given system. By adding certain components of the solution of certain linear system, our algorithm decreases the dimension of the deflation system in each step. Numerical experiments show the performance of our algorithm.