On Error Analysis of Systems of Linear Equations with Hadamard Coefficients

Year 2022, Volume: 11 Issue: 4, 1112 - 1116, 31.12.2022

Emine Tuğba Akyüz

https://doi.org/10.17798/bitlisfen.1180367

Abstract

In this study, error analysis for linear equation systems whose coefficients matrix is Hadamard matrix is discussed. In the Hx=f problem, the effect of the change in the elements in the f vector at the same rate and the change in the elements in the f vector at different rates were examined, and the relative error and absolute error equations for this system were given.

Keywords

Hadamard matrices, Error analysis, Relative error, Absolute error

References

• [1] R. K. R. Yarlagadda and J. E. Hershey, Matrix Analysis and Synthesis. USA: Kluwer Academic Publishers, 1997.
• [2] K. J. Horadam, Hadamard Matrices and Their Applications. Princeton University Press, 2007.
• [3] A. Hedayat and W. D. Wallis, “Hadamard matrices and their applications,” The Annals of Statistics, vol. 6, no. 6, pp. 1184–1238, 1978.
• [4] J. Seberry, B. J. Wysocki, and T. A. Wysocki, “On some applications of Hadamard matrices,” Metrika, vol. 62, pp. 221–239, 2005.
• [5] G. H. Golub and C. F. Van Loan, Matrix Computations (Third edition). Baltimore, MD: Johns Hopkins University Press, 1996.
• [6] L. W. Johnson and R. D. Riess, Numerical Analysis (Second eddition). Addison Wesley Publishing Company, 1982.
• [7] E. T. Akyüz, “Hadamard Matrices and the Ax=f Problem,” Selcuk University, Institute of Sciences, Konya, 2010.
• [8] D. R. Kincaid and E. W. Cheney, Numerical Analysis:Mathematics of Scientific Computing. Brooks/Cole Publishing Company, 1996.