158 reputation
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location Maryland
age 29
visits member for 3 years, 9 months
seen Apr 5 '12 at 15:53

Feb
17
awarded  Popular Question
Aug
17
comment Fast Algorithm For Adding An Equation To A System?
Nah, I actually found it funny when I realized how obvious an optimization I was missing.
Aug
17
awarded  Scholar
Aug
17
accepted Fast Algorithm For Adding An Equation To A System?
Aug
17
comment Fast Algorithm For Adding An Equation To A System?
(Slaps self in forehead.) Right, because matrix multiplication is associative. Thanks for your help and getting that through my thick head.
Aug
17
comment Fast Algorithm For Adding An Equation To A System?
Right, but this is only part of the algorithm. You're multiplying a column vector by a row vector to get an $NxN$ matrix, then you're multiplying that by another $NxN$ matrix. That's where it becomes $\mathcal{O}(N^3)$.
Aug
17
comment Fast Algorithm For Adding An Equation To A System?
But a column vector on the LHS times a row vector on the RHS produces an N*N matrix.
Aug
17
awarded  Commentator
Aug
17
comment Fast Algorithm For Adding An Equation To A System?
Right, but (C - V * A^-1 * U) is a scalar, A^-1 ^ U is a column vector and V is a row vector. Thus this multiplication produces a matrix.
Aug
17
comment Fast Algorithm For Adding An Equation To A System?
@Sirvarm: Look at equation 1 in the Wikipedia article you linked to. IIUC, A^-1 * U * (C - V * A^-1 * U) * V is an NxN matrix. You then multiply this monstrosity by A^-1, hence O(N^3).
Aug
17
comment Fast Algorithm For Adding An Equation To A System?
I saw that before I posted here. The problem is that the matrix multiplies involved in applying it make it also O(N^3). You have to multiply two NxN matrices at some point, which is an O(N^3) operation.
Aug
17
asked Fast Algorithm For Adding An Equation To A System?
Mar
29
comment What does matrix multiplication have to do with scalar multiplication?
No, I only know math related to engineering and probability/statistics. I know virtually nothing about the more theoretical branches. I've heard of abstract algebra, but know absolutely nothing about what it is. In hindsight I should have clarified this in my original post. Then again, your post makes me believe the reason matrix multiplication is called "multiplication" is much deeper than scientists, engineers, statisticians and generally people who aren't full-fledged mathematicians have the background to appreciate.
Mar
29
comment What does matrix multiplication have to do with scalar multiplication?
I'm sure this answer makes sense to a theoretical mathematician, but I asked the question from an engineer/applied mathematician's perspective. To me "multiplication", when unqualified, means scalar multiplication. From my perspective (this is admittedly subjective) if something is called multiplication, its properties should be similar to scalar multiplication in ways that are obvious in everyday contexts and don't require a Ph.D. in pure mathematics to appreciate.
Mar
29
comment What does matrix multiplication have to do with scalar multiplication?
@Arturo: Good point, but vector addition maps to scalar addition in a much more transparent way (it's just the component-wise sum) and preserves important properties like commutativity. It's subjective, but I think scalar vs. matrix multiplication stretches things much further than scalar vs. vector addition. Thus from a notational clarity point of view, denoting vector and scalar addition the same way is more reasonable than denoting scalar and matrix multiplication the same way.
Mar
29
asked What does matrix multiplication have to do with scalar multiplication?
Feb
7
comment High Dimensional Optimization Algorithm?
I thought of that (and read the article) as a way to solve the system of equations that Newton-Raphson gives me. However, it seems too slow to converge. If there is some other way I could be using it, please expand, as I'm not aware of it.
Feb
7
asked High Dimensional Optimization Algorithm?
Jan
21
comment Integrand non-negative everywhere, integral negative?
@Asaf: I thought of the geometric interpretation. It's just that this assumption is an intermediate step in a proof I'm working on, the proof needs to work even in pathological cases, and in my experience such geometric, intuitive arguments often fall apart in pathological cases.
Jan
21
comment Integrand non-negative everywhere, integral negative?
Thanks. This makes perfect sense. I just thought there might be some weird subtleties relating to Reimann vs. Lebesgue integrals, singularities, or other topics that I have only the vaguest clue about.