# Numerical linear algebra

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

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

The day, there ar mony tuils fur numerical linear algebra. Ane o the maist kenspeckle is MATLAB[13][14][15].

## References

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.