On a previous exam regarding numerical methods, we were given the ODE x' = -sgn(x), x(0) = 1/10. A subtask asked why Ode15s i.e. Newton's method fails after some time.
I answered that newton's method may fail due to singularity / rank-deficient matrix close to the solution. This was somehow wrong, feedback being: "The issue here is not rank-defficiency but the fact that the matrix does not exist at x=0. "
Aren't the two issues actually the same? What's the difference between newton's method failing due to rank-deficient matrix / singularity due to determinant vs. the matrix not existing at the particular solution?
I answered that newton's method may fail due to singularity / rank-deficient matrix close to the solution. This was somehow wrong, feedback being: "The issue here is not rank-defficiency but the fact that the matrix does not exist at x=0. "
Aren't the two issues actually the same? What's the difference between newton's method failing due to rank-deficient matrix / singularity due to determinant vs. the matrix not existing at the particular solution?
