Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering Applications
Quantum calculus can provide new insights into the nonlinear behaviour of functions and equations, addressing problems that may be difficult to tackle by classical calculus due to high nonlinearity. Iterative methods for solving nonlinear equations can benefit greatly from the mathematical theory an...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-02-01
|
| Series: | Applied Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-3417/14/4/1540 |
| _version_ | 1797299055638872064 |
|---|---|
| author | Mudassir Shams Bruno Carpentieri |
| author_facet | Mudassir Shams Bruno Carpentieri |
| author_sort | Mudassir Shams |
| collection | DOAJ |
| description | Quantum calculus can provide new insights into the nonlinear behaviour of functions and equations, addressing problems that may be difficult to tackle by classical calculus due to high nonlinearity. Iterative methods for solving nonlinear equations can benefit greatly from the mathematical theory and tools provided by quantum calculus, e.g., using the concept of q-derivatives, which extends beyond classical derivatives. In this paper, we develop parallel numerical root-finding algorithms that approximate all distinct roots of nonlinear equations by utilizing q-analogies of the function derivative. Furthermore, we utilize neural networks to accelerate the convergence rate by providing accurate initial guesses for our parallel schemes. The global convergence of the q-parallel numerical techniques is demonstrated using random initial approximations on selected biomedical applications, and the efficiency, stability, and consistency of the proposed hybrid numerical schemes are analyzed. |
| first_indexed | 2024-03-07T22:44:01Z |
| format | Article |
| id | doaj.art-dc11391fd84f4039bd25babc2c043552 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-07T22:44:01Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-dc11391fd84f4039bd25babc2c0435522024-02-23T15:06:20ZengMDPI AGApplied Sciences2076-34172024-02-01144154010.3390/app14041540Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering ApplicationsMudassir Shams0Bruno Carpentieri1Faculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bolzano, ItalyFaculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bolzano, ItalyQuantum calculus can provide new insights into the nonlinear behaviour of functions and equations, addressing problems that may be difficult to tackle by classical calculus due to high nonlinearity. Iterative methods for solving nonlinear equations can benefit greatly from the mathematical theory and tools provided by quantum calculus, e.g., using the concept of q-derivatives, which extends beyond classical derivatives. In this paper, we develop parallel numerical root-finding algorithms that approximate all distinct roots of nonlinear equations by utilizing q-analogies of the function derivative. Furthermore, we utilize neural networks to accelerate the convergence rate by providing accurate initial guesses for our parallel schemes. The global convergence of the q-parallel numerical techniques is demonstrated using random initial approximations on selected biomedical applications, and the efficiency, stability, and consistency of the proposed hybrid numerical schemes are analyzed.https://www.mdpi.com/2076-3417/14/4/1540neural networkq-iterative schemesq-Taylor’s seriesCPU-Timeconvergence ratebiomedical engineering applications |
| spellingShingle | Mudassir Shams Bruno Carpentieri Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering Applications Applied Sciences neural network q-iterative schemes q-Taylor’s series CPU-Time convergence rate biomedical engineering applications |
| title | Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering Applications |
| title_full | Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering Applications |
| title_fullStr | Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering Applications |
| title_full_unstemmed | Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering Applications |
| title_short | Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering Applications |
| title_sort | q analogues of parallel numerical scheme based on neural networks and their engineering applications |
| topic | neural network q-iterative schemes q-Taylor’s series CPU-Time convergence rate biomedical engineering applications |
| url | https://www.mdpi.com/2076-3417/14/4/1540 |
| work_keys_str_mv | AT mudassirshams qanaloguesofparallelnumericalschemebasedonneuralnetworksandtheirengineeringapplications AT brunocarpentieri qanaloguesofparallelnumericalschemebasedonneuralnetworksandtheirengineeringapplications |