For liear equation y = A*x, why use Gaussian elimination to solve the linear equation other than calculating multiplication of inverse of A and y directly?
Because we would not like to use a sledgehammer to crack a peanut. Matrix inversion is a more complex problem than a Gauss elimination.
Dear Bo Li ,
Look the link, may be useful.
http://www.purplemath.com/modules/systlin6.htm
http://www.dummies.com/education/math/calculus/how-to-use-gaussian-elimination-to-solve-systems-of-equations/
http://www.dummies.com/education/math/calculus/how-to-use-gaussian-elimination-to-solve-systems-of-equations/
Regards, Shafagat
Because we would not like to use a sledgehammer to crack a peanut. Matrix inversion is a more complex problem than a Gauss elimination.
Gauss elimination is nearly an immediate metod to solve linear equations. You need not to calculate the determinant nor the inverse matrix. The inversion carrries often serious problems with rounding specially whether the eigenvalues are sparse. I think inversion shoud be considered only when any other alternative is not affordable
Matrix inversion cost more time than you think, and may cause pivot error. Elimination process transfer the inversion problem to a equation set problem which make the work easier, faster and more accurate.
A book talks about numerical method in detail:
Numerical Analysis, by Richard L. Burden, J. Douglas Faires,
- Badges
- Science topic