BiCGStab, VPAStab and an adaptation to mildly nonlinear systems

The key equations of BiCGStab are summarised to show its connections with Padé and vector-Padé approximation. These considerations lead naturally to stabilised vector-Padé approximation of a vector-valued function (VPAStab), and an algorithm for the acceleration of convergence of a linearly generated sequence of vectors. A generalisation of this algorithm for the acceleration of convergence of a nonlinearly generated system is proposed here, and comparative numerical results are given.