On solving quasilinear elliptic equations by variational methods, using piecewise polynomial trial functions

Imperial Users onl

Stability of Gaussian elimination without pivoting on tridiagonal Toeplitz matrices

AbstractUsing the simple vehicle of tridiagonal Toeplitz matrices, the question of whether one must pivot during the Gauss elimination procedure is examined. An exact expression for the multipliers encountered during the elimination process is given. It is then shown that for a prototype Helmholtz problem, one cannot guarantee that elimination without pivoting is stable