Acceleration Convergence of Sequence of Bicomplex Numbers

In this article, we explore three fundamental concepts: acceleration convergence, logarithmic convergence, and subsequence transformation in the context of bicomplex number sequences.Acceleration convergence is a technique for speeding up the convergence of slowly convergent sequences, particularly in iterative methods.We examine how this method can be adapted for sequences of bicomplex numbers by leveraging their unique algebraic structure.Logarithmic convergence, in which a sequence converges logarithmically, is analyzed in the bicomplex framework.Additionally, subsequence transformations are introduced as tools for manipulating and extracting useful convergent subsequences from a given bicomplex sequence.