875 reputation
423
bio website math.utep.edu/faculty/…
location El Paso, TX
age 33
visits member for 2 years, 7 months
seen Aug 6 at 20:54

Computational Science PhD student
University of Texas El Paso
Climate & Energy Science Student Organization President
National Energy Technology Laboratory Intern
NSF LSAMP Fellow


Aug
31
comment Verifying an error estimate on a multidimensional function using its jacobian
Thanks, copper.hat! :)
Aug
31
accepted Verifying an error estimate on a multidimensional function using its jacobian
Aug
31
comment Verifying an error estimate on a multidimensional function using its jacobian
You're answer makes a lot sense now! Just one little question: I'm not quite sure I understand how we can make the assumption that $\epsilon \le ||J(x^*)||$ "without loss of generality". Could you elaborate on that? What allows us to make such a claim?
Aug
31
comment Verifying an error estimate on a multidimensional function using its jacobian
I think I understand it now... The main purpose of the statement in the first line of the second paragraph is to ensure that $||x+t(x^*-x)-x||$ is in the ball so that continuity ensures that we can bound $||J(x+t(x^*-x)-x)-J(x)||$ by epsilon. It's a subtle detail that I just couldn't see at first.
Aug
31
comment Verifying an error estimate on a multidimensional function using its jacobian
Hi copper.hat. In the second line of the second paragraph, you wrote $||x+t(x^*-x) -x||$, but I think you meant to write $||x+t(x^*-x) -x^*||$. Otherwise, $||x+t(x^*-x) -x||=t||x^*-x||$. Do you agree?
Aug
31
revised Verifying an error estimate on a multidimensional function using its jacobian
corrected slight error in notation
Aug
31
accepted Sufficiency to prove the convergence of a sequence using even and odd terms
Aug
31
revised Verifying an error estimate on a multidimensional function using its jacobian
corrected formatting
Aug
31
asked Verifying an error estimate on a multidimensional function using its jacobian
Aug
30
comment How do I obtain an appropriate energy functional from the weak formulation of a partial differential equation?
Substituting v=u into the weak formulation accounts for most of the functional $F(u)$ except for the term $\frac{1}{2}au^2$. Where did the $\frac{1}{2}$ come from?
Aug
30
comment Applying a multidimensional variant of Taylor's Theorem
Thanks so much, shoda! :)
Aug
30
accepted Applying a multidimensional variant of Taylor's Theorem
Aug
30
comment Applying a multidimensional variant of Taylor's Theorem
@shoda: Yes, you are correct. In the process of copying and pasting, I neglected to change the limits. Thanks for the heads up! :)
Aug
30
revised Applying a multidimensional variant of Taylor's Theorem
deleted 4 characters in body
Aug
30
asked Applying a multidimensional variant of Taylor's Theorem
Aug
27
asked Sufficiency to prove the convergence of a sequence using even and odd terms
Aug
23
revised Help solving differential equation
Edited for easier readability
Aug
23
suggested suggested edit on Help solving differential equation
Aug
23
comment Help solving differential equation
There are a variety of ways to solve it. Are you looking for an analytical solution or a numerical one? Also, have you consulted any introductory ordinary differential equations books? This is a classic problem with well studied properties and I'm sure you can find more detailed information in a good undergraduate textbook.
Aug
18
revised Understanding how to state the Karush-Kuhn-Tucker Conditions for a given problem
removed statement to reflect corrections made in original question