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Home > Archives > Volume 20, No 8 (2022) > Article

DOI: 10.14704/nq.2022.20.8.NQ44521

Development Of an Android Mobile Phone Application for Finding Closed-Loop, Analytical Solutions to Dense Linear, Algebraic Equations for The Purpose of Mathematical Modelling in Healthcare and Neuroscience Research

Santhosh Kumar Rajamani, Radha Srinivasan Iyer

Abstract

Closed-loop, analytical solution of Linear, algebraic equation containing many unknown variables are found in many mathematical modeling equations and network analysis involved in healthcare and neuroscience research. Finding unique, analytical solution for linear, algebraic equations has diverse application in many fields. Computation of unique, non-trivial solutions to large array containing several variables is a computationally overwhelming task. The paper begins by introducing the concept of network analysis in modelling for healthcare and neuroscience research. A simple example of network modelling is the logistics of delivering vaccine like COVID19 from a company to Primary health center while maintaining cold-storage of the vaccine. This is followed by explanation of the working of computationally efficient, best-practice LU Decomposition with partial pivoting algorithm to solve dense linear equations. This is followed by narration of building, testing, obfuscation, compiling and release of an Android Graphic user interface application implementing the above methods. The final part of the paper examines the exceptional accuracy and efficiency of solving, dense matrix equations on Android Run Time machine using this approach. The calculated Poisson modelling of probability of Stochastic, Singularity event is = πŸ‘. πŸπŸ” Γ— πŸπŸŽβˆ’πŸ—π’‘er floating point operation a number derived after running πŸπŸ“, πŸ”πŸπŸ“, 𝟎𝟎𝟎, 𝟎𝟎𝟎 floating-point operation runs. The mean execution time was 88.534 𝒔𝒆𝒄𝒐𝒏𝒅𝒔 , for solving matrix equation [𝑨]π’˜π’Šπ’•π’‰N=60 variables in performing π‘΅πŸ‘=216000 computations. The whole working Android application containing many other tools is hosted on the GitHub and Figshare platforms along with additional graphs, dataset, Java, and Python programs used to complete this study.

Keywords

Decomposition, Matrix algebra, Mathematical modelling, Computer aided algebra, Linear algebra, Linear equations

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