Ah I see that makes sense. Thank you very much On Monday, June 8, 2015, Jed Brown <[email protected]> wrote:
> Justin Chang <[email protected] <javascript:;>> 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. >
