  Nonlinear mapping is an essential and common demand in online systems, such
as sensor systems and mobile phones. Accelerating nonlinear mapping will
directly speed up online systems. Previously the authors of this paper proposed
a Dendrite Net (DD) with enormously lower time complexity than the existing
nonlinear mapping algorithms; however, there still are redundant calculations
in DD. This paper presents a DD with an acceleration module (AC) to accelerate
nonlinear mapping further. We conduct three experiments to verify whether DD
with AC has lower time complexity while retaining DD's nonlinear mapping
properties and system identification properties: The first experiment is the
precision and identification of unary nonlinear mapping, reflecting the
calculation performance using DD with AC for basic functions in online systems.
The second experiment is the mapping precision and identification of the
multi-input nonlinear system, reflecting the performance for designing online
systems via DD with AC. Finally, this paper compares the time complexity of DD
and DD with AC and analyzes the theoretical reasons through repeated
experiments. Results: DD with AC retains DD's excellent mapping and
identification properties and has lower time complexity. Significance: DD with
AC can be used for most engineering systems, such as sensor systems, and will
speed up computation in these online systems. The code of DD with AC is
available on https://github.com/liugang1234567/Gang-neuron
