You are quite correct about stability but I didn't want to get into technical details. And indeed you bring up correctly that such numerical issues mustn’t be t

You are quite correct about stability but I didn't want to get into technical details. And indeed you bring up correctly that such numerical issues mustn’t be treated lightly. I don't do computer graphics and the matrices I deal with are well conditioned such that problems of stability that arise due to linear algebra routines are negligible. In my simulations, instability arises due to the wrong time-stepping scheme, which is a completely different issue. And good recommendation by Strang. I believe he has some fantastic MIT OpenCourse lectures on numerical linear algebra as well.