CFP last date
20 December 2024
Reseach Article

Computational Mathematics: Solving Complex Problems with the Latest Techniques

by Romal Bharatkumar Patel
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 184 - Number 46
Year of Publication: 2023
Authors: Romal Bharatkumar Patel
10.5120/ijca2023922574

Romal Bharatkumar Patel . Computational Mathematics: Solving Complex Problems with the Latest Techniques. International Journal of Computer Applications. 184, 46 ( Feb 2023), 37-43. DOI=10.5120/ijca2023922574

@article{ 10.5120/ijca2023922574,
author = { Romal Bharatkumar Patel },
title = { Computational Mathematics: Solving Complex Problems with the Latest Techniques },
journal = { International Journal of Computer Applications },
issue_date = { Feb 2023 },
volume = { 184 },
number = { 46 },
month = { Feb },
year = { 2023 },
issn = { 0975-8887 },
pages = { 37-43 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume184/number46/32618-2023922574/ },
doi = { 10.5120/ijca2023922574 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T01:24:09.836364+05:30
%A Romal Bharatkumar Patel
%T Computational Mathematics: Solving Complex Problems with the Latest Techniques
%J International Journal of Computer Applications
%@ 0975-8887
%V 184
%N 46
%P 37-43
%D 2023
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Computational mathematics is a field that involves the use of mathematical techniques and algorithms to solve problems in science, engineering, and other fields. This includes a wide range of topics, such as numerical analysis, scientific computing, optimization, and machine learning. Numerical methods and algorithms play a crucial role in computational mathematics, as they allow for the approximate solution of complex problems that may not have an exact solution. Mathematical models are also an important tool in computational mathematics, as they provide a framework for understanding and predicting real-world phenomena. Machine learning and data analysis techniques are increasingly being used in computational mathematics to analyze large datasets and extract insights. High-performance computing and cloud computing are also key areas within computational mathematics, as they enable the processing of large amounts of data and the running of complex simulations. Finally, emerging technologies such as deep learning and quantum computing hold great potential for advancing the field of computational mathematics in the future.

References
  1. Burden, R. L., & Faires, J. D. (2011). Numerical analysis (9th ed.). Boston, MA: Brooks/Cole. https://www.amazon.com/Numerical-Analysis-9th-Book-Only/dp/B0059JHM6M
  2. Heath, M. T. (2002). Scientific computing: An introductory survey (2nd ed.). New York, NY: McGraw-Hill. https://www.amazon.com/Scientific-Computing-Introductory-Survey-Revised/dp/1611975573/ref=sr_1_1?crid=38XGH4JUFP4PQ&keywords=Scientific+computing&qid=1673244999&s=b ooks&sprefix=scientific+computing%2Cstripbooks-intl-ship%2C711&sr=1-1
  3. Luenberger, D. G. (2008). Optimization by vector space methods (2nd ed.). New York, NY: Wiley. https://www.amazon.com/Optimization-Vector-Space-Methods-Luenberger/dp/047118117X/ref=sr_1_1?crid=DKD35559EP13&keywords=Optimization+by+vector+space+methods+%282nd+ed.%29&qid=1673245203&s=books&sprefix=optimization+by+vector+space+methods+2nd+ed.+%2Cstripb ooks-intl-ship %2C652&sr=1-1
  4. Bishop, C. M. (2006). Pattern recognition and machine learning (1st ed.). New York, NY: Springer. https://www.amazon.com/Pattern-Recognition-Learning-Information-Statistics/dp/0387310738 Nocedal, J., & Wright, S. J. (2006). Numerical optimization (2nd ed.). New York, NY: Springer. https://www.amazon.com/Numerical-Optimization-Second-Springer-Science/dp/0387303030
  5. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical recipes: The art of scientific computing (3rd ed.). Cambridge, UK: Cambridge University Press. https://www.amazon.com/Numerical-Recipes-Art-Scientific-Computing/dp/0521880688
  6. Francis B. Hildebrand. Introduction to Numerical Analysis: Dover Publications; Second edition (April 26, 2013), (Dover Books on Mathematics) Second Edition, Kindle Edition https://www.amazon.com/Introduction-Numerical-Analysis-Second-Mathematics/dp/0486653633
  7. Lloyd N. Trefethen (Author). Spectral Methods in MATLAB (Software, Environments, Tools) 62026th Edition. Philadelphia, PA: Society for Industrial and Applied Mathematics. https://www.amazon.com/Spectral-Methods-MATLAB-Software-Environments/dp/0898714656
  8. Boyd, S., & Vandenberghe, L. (2004). Convex optimization. New York, NY: Cambridge University Press. https://www.amazon.com/Convex-Optimization-Corrections-2008-Stephen/dp/0521833787/ref=sr_1_1?crid=31O908LGFDRGR&keywords=Convex+optimization&qid=1673248411&s= books&sprefix=convex+optimization%2Cstripbooks-intl-ship%2C890&sr=1-1
  9. Katta G. Murty (September 1983). Linear programming. NY: John Wiley & Sons. https://www.wiley.com/en-sg/Linear+Programming-p-9780471097259
  10. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical recipes: The art of scientific computing (3rd ed.). Cambridge, UK: Cambridge University Press. https://www.amazon.com/Numerical-Recipes-Scientific-Computing-Press/dp/0521880688
  11. Gander, W., & Gautschi, W. (2000). Numerical analysis: An introduction (2nd ed.). New York, NY: Birkhäuser. https://www.amazon.com/Numerical-Analysis-Introduction-Walter-Gautschi/dp/3764338954
  12. Trefethen, L. N. (2000). Spectral methods in MATLAB (1st ed.). Philadelphia, PA: Society for Industrial and Applied Mathematics. https://www.amazon.com/Spectral-Methods-MATLAB-Lloyd-Trefethen/dp/0898714754
  13. Boyd, S., & Vandenberghe, L. (2004). Convex optimization. New York, NY: Cambridge University Press. https://www.amazon.com/Convex-Optimization-Stephen-Boyd/dp/0521833787
  14. Murty, M. N. (1997). Linear programming. New York, NY: John Wiley & Sons. https://www.amazon.com/Linear-Programming-John-Wiley-Series-Operations/dp/0471144269
  15. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical recipes: The art of scientific computing (3rd ed.). Cambridge, UK: Cambridge University Press. https://www.amazon.com/Numerical-Recipes-Scientific-Computing-Press/dp/0521880688
  16. Gander, W., & Gautschi, W. (2000). Numerical analysis: An introduction (2nd ed.). New York, NY: Birkhäuser. https://www.amazon.com/Numerical-Analysis-Introduction-Walter-Gautschi/dp/3764338954
  17. Burden, R. L., & Faires, J. D. (2011). Numerical analysis (9th ed.). Boston, MA: Brooks/Cole. https://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/0534382169
  18. Heath, M. T. (2002). Scientific computing: An introductory survey (2nd ed.). New York, NY: McGraw-Hill. https://www.amazon.com/Scientific-Computing-Michael-T-Heath/dp/0072399104
  19. Luenberger, D. G. (2008). Optimization by vector space methods (2nd ed.). New York, NY: Wiley. https://www.amazon.com/Optimization-Vector-Space-Methods-Luenberger/dp/047118117X
  20. Bishop, C. M. (2006). Pattern recognition and machine learning (1st ed.). New York, NY: Springer. https://www.amazon.com/Pattern-Recognition-Learning-Information-Statistics/dp/0387310738
  21. Nocedal, J.,& Wright, S. J. (2006). Numerical optimization (2nd ed.). New York, NY: Springer. https://www.amazon.com/Numerical-Optimization-Springer-Science-Business/dp/0387303030
  22. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical recipes: The art of scientific computing (3rd ed.). Cambridge, UK: Cambridge University Press. https://www.amazon.com/Numerical-Recipes-3rd-Scientific-Computing/dp/0521880688
  23. Gander, W., & Gautschi, W. (2000). Numerical analysis: An introduction (2nd ed.). New York, NY: Birkhäuser. https://www.amazon.com/Numerical-Analysis-Introduction-Walter-Gautschi/dp/3764338954
  24. Trefethen, L. N. (2000). Spectral methods in MATLAB (1st ed.). Philadelphia, PA: Society for Industrial and Applied Mathematics. https://www.amazon.com/Spectral-Software-Environments-Trefethen-2000-07-01/dp/B01K0S23SI
  25. Stephen Boyd, Lieven Vandenberghe (2004). Convex Optimization 1st Edition, Kindle Edition. New York, NY: Cambridge University Press; 1st edition (March 8, 2004) https://www.amazon.com/Convex-Optimization-Stephen-Boyd-ebook/dp/B00E3UR2KE
  26. Anish K Sah, (April 16, 2022). Gradient Descent: A Bank Loan Story. Kindle Edition. https://www.amazon.com/Gradient-Descent-Bank-Loan-Story-ebook/dp/B09Y4L87FV/ref=sr_1_1?crid=33FVBG1UVL65T&keywords=Gradient+descent&qid=1673251031&s=digital - text&sprefix=gradient+descent%2Cdigital-text%2C694&sr=1-1
  27. Back propagation. https://en.wikipedia.org/wiki/Backpropagation
  28. Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. https://arxiv.org/abs/1412.6980
  29. Support vector machine. https://en.wikipedia.org/wiki/Support_vector_machine
  30. Cloud computing. https://en.wikipedia.org/wiki/Cloud_computing
  31. Data mining. https://en.wikipedia.org/wiki/Data_mining
  32. Robotics.https://en.wikipedia.org/wiki/Robotics
  33. Internet of things. https://en.wikipedia.org/wiki/Internet_of_things
  34. Cybersecurity.https://en.wikipedia.org/wiki/CybersecurityTuring, A. M. (1950). Computing machinery and intelligence.https://redirect.cs.umbc.edu/courses/471/papers/turing.pdf
  35. Hopcroft, J. E., & Ullman, J. D. (1979). Introduction to automata theory, languages, and computation. Reading, MA: Addison-Wesley. https://www-2.dc.uba.ar/staff/becher/Hopcroft-Motwani-Ullman-2001.pdf
  36. Donald Knuth. (1997). The art of computer programming, vol. 1: Fundamental algorithms (3rd ed.). Reading, MA: Addison-Wesley. https://en.wikipedia.org/w/index.php?go=Go&search=Knuth%2C+D.+E.+%281997%29.+The+art+of+computer+progr amming%2C+vol.+1%3A+Fundamental+algorithms+%283rd+ed.%29.+Reading%2C+MA%3A+Addison-Wesley.&title=Special:Search&ns0=1
  37. Sedgewick, R. (2011). Algorithms (4th ed.). Upper Saddle River, NJ: Pearson Education. https://www.amazon.com/Algorithms-4th-Robert-Sedgewick/dp/032157351X
  38. Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to algorithms (3rd ed.). Cambridge, MA: MIT Press.https://www.amazon.com/Introduction-Algorithms-3rd-MIT-Press/dp/0262033844
  39. Watson, J. (1953). The double helix: A personal account of the discovery of the structure of DNA. New York, NY: Signet. https://www.amazon.com/Double-Helix-Personal-Discovery-Structure/dp/074321630X
  40. A mathematical theory of communication. https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication#:~:text=%22A%20Mathematical%20Theory %20of %20Communication,the%20generality%20of%20this%20work.
  41. Algorithm 97: Shortest path https://dl.acm.org/doi/10.1145/367766.368168
  42. Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269-271. https://link.springer.com/article/10.1007/BF01386390
  43. Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society, 7(1), 48-50. https://scirp.org/reference/referencespapers.aspx?referenceid=1449476
  44. Prim, R. C. (1957). Shortest connection networks and some generalizations. Bell System Technical Journal, 36(6), 1389-1401. https://ieeexplore.ieee.org/document/6773228
  45. Johnson, D. S. (1977). Efficient algorithms for shortest paths in sparse networks. Journal of the ACM, 24(1), 1-13. https://dl.acm.org/doi/abs/10.1145/321992.321993
  46. Viterbi, A. J. (1967). Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory, 13(2), 260-269. https://ieeexplore.ieee.org/document/1054010
  47. Gallager, R. G. (1963). Low-density parity-check codes. https://web.stanford.edu/class/ee388/papers/ldpc.pdf
  48. Ashikhmin, A., & Knill, E. (2000). Nonbinary quantum stabilizer codes. IEEE Transactions on Information Theory, 47(7), 3065-3072 https://ieeexplore.ieee.org/document/959288
Index Terms

Computer Science
Information Sciences

Keywords

Big data Artificial intelligence Deep learning Cloud computing High-performance computing Data Science Natural language processing Computer vision Blockchain Quantum computing Data mining Robotics Internet of Things (IoT) Cyber security