The detailed derivation is tedious and of little interest to this project, so we report only the main results in the following.
For the SNLS model 8, J x) is 2 × 2. Again, the gradient derivations are tedious but symbolic exercises not reproduced here.
The symbolic approach turns out to be roughly two times faster, at the price of rather tedious and error-prone manual derivation of the mathematical equations.
The proposed method has several remarkable features: the use of AD techniques avoids tedious and error-prone manual derivation and programming; duality is strictly preserved so that consistent and highly accurate discrete sensitivities can be obtained; and comparable efficiency to hand-coded implementation can be achieved.
Although the derivation process is quite tedious, we show analytically that the inverse transform can be found exactly and their resulting expressions are surprisingly neat and compact.
For the system with large DOF, the derivation and linearization of EOM are very tedious and difficult.
In the case of compressible solvers, the use of high-order numerical schemes combined with complicated governing equations makes the derivation of efficient procedures a challenging and often tedious undertaking.
Since the derivation of the variance expression for frequency selective channel case is tedious, we used simulations to estimate the same.
In order to explain this, a complete analytical derivation of the noise distribution for z ̂ would be long and tedious, so we restrict ourselves to a qualitative justification which is provided in the Appendix.
"The author … introduces the mathematical methods essential to understanding and applying general relativity…but leaves to more advanced references derivations that a beginning student would likely find overly long and tedious….
