A major source of numerical errors in digital computers arises from the way numbers are stored and managed in computers. Before diving into examining numerical errors, it is necessary to briefly look into how numbers are handled on digital computers.

 

  1. Barrett, R., Berry, M., Chan, T., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., and van der Vorst, H., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, Pennsylvania, 1993.
  2. Burden, R.L. and Faires, J.D., Numerical Analysis, nineth edition, Broks/Cole, Cengage, Boston, MA,
  3. Darve, E. and Wootters, M., Numerical Linear Algebra with Julia, SIAM, Philadelphia, 2021.
  4. Krylov, A. N. (1931). "О численном решении уравнения, которым в технических вопросах определяются частоты малых колебаний материальных систем" [On the Numerical Solution of Equation by Which are Determined in Technical Problems the Frequencies of Small Vibrations of Material Systems]. Izvestiia Akademii Nauk SSSR (in Russian). 7 (4): 491–539.
  5. Hestenes, Magnus R.; Stiefel, Eduard (December 1952). "Methods of Conjugate Gradients for Solving Linear Systems" (PDF). Journal of Research of the National Bureau of Standards. 49 (6): 409. doi:10.6028/jres.049.044
  6. Lanczos, C. (1950). "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators" (PDF). Journal of Research of the National Bureau of Standards. 45 (4): 255–282. doi:10.6028/jres.045.026
  7. Loehr, N., Advanced Linear Algebra, CRC Press, 2014.
  8. Kelley, C.T., Iterative Methods for Optimization, SIAM, Philadelphia, 1999.
  9. Shewchuk, J.R., An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, 1994, School of Computer Science, Carnegie Mellon University.
  10. <
  11. Shi, X., Wei, Y., and Zhang, W., Convergence of General Nonstationary Iterative Methods for Solving Singular Linear Equations, Taylor & Francis Online, Volume 38, Issue 11,
  12. /ol>