The Adomian’s decomposition method (ADM) is a solution method with a wide range of applications including the solution of algebraic, differential, integral and integro-differential equations or system of equations. This method was first introduced by Adomian [1, 2] in the beginning of the 1980’s. In this method the solution is considered as an rapidly converging, infinite series. The convergenc...

This paper discusses how to control the accuracy of inexact matrix-vector products in restarted GMRES. We will show that the GMRES iterations can be performed with relatively low accuracy. Furthermore, we will study how to compute the residual at restart and propose suitable strategies to control the accuracy of the matrix-vector products in this computation.

Self-attention networks have shown remarkable progress in computer vision tasks such as image classification. The main benefit of the self-attention mechanism is ability to capture long-range feature interactions attention-maps. However, computation attention-maps requires a learnable key, query, and positional encoding, whose usage often not intuitive computationally expensive. To mitigate thi...

We prove that the cycle–convergence of the restarted GMRES applied to a system of linear equations with a normal coefficient matrix is sublinear.