RcdMathLib: An Open Source Software Library for Computing on Resource-Limited Devices.

Area of Science:

• Computational Mathematics
• Embedded Systems Engineering
• Internet of Things (IoT)

Background:

• Multivariate systems require significant computational resources, limiting their application on low-cost, resource-constrained devices.
• Decentralized processing and efficient algorithms are crucial for enabling ubiquitous computing and advanced Internet of Things (IoT) applications.
• Existing libraries may not be optimized for on-the-fly computation on embedded systems.

Purpose of the Study:

• To develop an open-source library, RcdMathLib, for solving multivariate linear and nonlinear systems.
• To enable on-the-fly computation on low-cost and resource-constrained devices, facilitating IoT implementations.
• To provide a modular and layer-based library with diverse functionalities for algebraic operations, data processing, and system optimization.

Main Methods:

• Development of a modular, layer-based open-source library (RcdMathLib).
• Implementation of efficient decomposition approaches, including Singular Value Decomposition (SVD), for solving linear and nonlinear equations.
• Integration of optimization methods like Gauss-Newton and Levenberg-Marquardt for regression, smoothing, and curve fitting.
• Inclusion of a positioning module with trilateration algorithms and multipath error reduction for IoT devices.

Main Results:

• RcdMathLib successfully supports on-the-fly computing on microcontrollers and other resource-constrained devices.
• The library enables the solution of multivariate linear and nonlinear systems using efficient decomposition and optimization techniques.
• A dedicated positioning module allows for accurate device location computation and error optimization in IoT networks.
• The library has been implemented and tested on both resource-limited IoT devices and full-fledged operating systems.

Conclusions:

• RcdMathLib provides a versatile and efficient solution for complex mathematical computations in resource-constrained environments.
• The library is a significant step towards ubiquitous computing, enabling the development of sophisticated IoT applications.
• Its open-source nature and modular design promote accessibility and further development within the scientific and engineering communities.