Computer data processing method of map manifold based on derivative transfer approach

Abstract

SummaryWith the rapid development of Internet technology and the rapid upgrade of hardware devices such as computers and smartphones, the data processed by computers often presents a high dimension. How to reduce data dimension and improve data processing speed is a hot research topic in the computer field. One shortcoming of one‐dimensional manifold calculation methods via sequence points is that the position of new points on the manifold is determined by searching the existing manifold by dichotomy, which is tedious and time‐consuming. This paper improved this method based on derivative transfer. According to the calculation results of one‐dimensional stable and unstable manifolds, they exhibited a special property, that is, for any point on the manifold orbit, its image and preimage must also be on the manifold orbit. Based on this, the derivative transfer method was used to improve the calculation of one‐dimensional manifolds for the map, and a three‐step calculation method of “prediction‐correction‐accuracy verification” was proposed. Then this method was applied to the simulation of high‐dimensional manifolds. The simulation results revealed that the proposed method refined the manifold calculation and greatly enhanced the computation speed.