Numerical linear algebra

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I the field o numerical analysis, numerical linear algebra is an area tae study methods tae solve problems i linear algebra bi computers[1][2][3][4][5][6].

Errors[eedit | eedit soorce]

Numerical errors can occur i any kynd o numerical computation includin the area o numerical linear algebra. Errors i numerical linear algebra are considerit i another area callit "validatit numerics"[7][8][9][10][11][12].

Saftware[eedit | eedit soorce]

Today, thare are many tools for numerical linear algebra. Ane o the most famous ane is MATLAB[13][14][15].

References[eedit | eedit soorce]

  1. Demmel, J. W. (1997). Applied numerical linear algebra. SIAM.
  2. Ciarlet, P. G., Miara, B., & Thomas, J. M. (1989). Introduction to numerical linear algebra and optimization. Cambridge University Press.
  3. Trefethen, Lloyd; Bau III, David (1997). Numerical Linear Algebra (1st ed.). Philadelphia: SIAM.
  4. Saad, Yousef (2003). Iterative methods for sparse linear systems (2nd ed.). SIAM.
  5. David S. Watkins (2008), The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods, SIAM.
  6. Higham, N. J. (2008). Functions of matrices: theory and computation. SIAM.
  7. Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287-449.
  8. Yamamoto, T. (1984). Error bounds for approximate solutions of systems of equations. Japan Journal of Applied Mathematics, 1(1), 157.
  9. Oishi, S., & Rump, S. M. (2002). Fast verification of solutions of matrix equations. Numerische Mathematik, 90(4), 755-773.
  10. Yamamoto, T. (1980). Error bounds for computed eigenvalues and eigenvectors. Numerische Mathematik, 34(2), 189-199.
  11. Yamamoto, T. (1982). Error bounds for computed eigenvalues and eigenvectors. II. Numerische Mathematik, 40(2), 201-206.
  12. Mayer, G. (1994). Result verification for eigenvectors and eigenvalues. Topics in Validated Computations, Elsevier, Amsterdam, 209-276.
  13. Gilat, Amos (2004). MATLAB: An Introduction with Applications 2nd Edition. John Wiley & Sons.
  14. Quarteroni, Alfio; Saleri, Fausto (2006). Scientific Computing with MATLAB and Octave. Springer.
  15. Gander, W., & Hrebicek, J. (Eds.). (2011). Solving problems in scientific computing using Maple and Matlab®. Springer Science & Business Media.

External Links[eedit | eedit soorce]

Further Reading[eedit | eedit soorce]

  • Golub, Gene H.; Van Loan, Charles F. (1996). Matrix Computations (3rd ed.). Baltimore: The Johns Hopkins University Press.
  • Matrix Iterative Analysis, Varga, Richard S., Springer, 2000.
  • Higham, N. J. (2002). Accuracy and stability of numerical algorithms. Society for Industrial and Applied Mathematics.
  • Liesen, J., & Strakos, Z. (2012). Krylov subspace methods: principles and analysis. OUP Oxford.