Justin Chang <[email protected]> writes: > Jed, > > Thank you for your response. I agree completely with all that you said. I > just wonder what would happen if I attempted to use the TAO routines after > forming the Jacobian J and residual r arising from the advection diffusion > equation. > > In my current (linear) diffusion framework, i have the following objective > function and gradient vector: > > f = \frac{1}{2} x \cdot J*x + x\cdot[r - J*x^(0)]
If J is non-symmetric, then you're no longer looking for a minimum of this functional. Let's take a prototypical example in 2 variables J = [0 1; -1 0] Now the J-"inner product" conj(x) \cdot J x = 0 for all real-valued x. (I'll assume you're working over the reals.) Similarly, the J-"inner product" with J = [1 1; -1 1] is identical to that with J = eye(2), but obviously you want the anti-symmetric part to affect your solution. In short, none of this makes mathematical sense in the way you intend if J is nonsymmetric.
signature.asc
Description: PGP signature
