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Jun
21
awarded  Nice Answer
Jun
5
awarded  Good Answer
Jun
1
comment Real world application of Fourier series
@AreaMan I was talking about the decrease in the magnitude of fourier coefficients. Basically, the smoother the function is, the faster the fourier coefficients will decrease in magnitude and hence we need fewer terms to approximate the original function well.
Apr
30
awarded  Yearling
Jan
16
comment How to calculate the approximate zero of any polynomial function without Newton's Method?
@Xoque55 Newton's method can work for $x^2+1=0$ if your starting point has a nonzero imaginary part.
Jan
8
awarded  Famous Question
Jan
4
awarded  Popular Question
Dec
17
answered What are some applications of elementary linear algebra outside of math?
Oct
29
accepted How to fill in these steps to evaluate this Gaussian integral?
Sep
23
comment Really advanced techniques of integration (definite or indefinite)
+1 Risch's algorithm has a 100 page summary. Talk about an advanced technique.
Sep
4
accepted Transforming a nonlinear system to a linear system
Sep
4
comment Transforming a nonlinear system to a linear system
It is part of a much larger nonlinear regression problem. But this can also stand alone on its own. I have three points and I want to determine $a$, $b$, and $c$ so that the Lorentzian curve goes through those three points. If I solve the nonlinear system, I need iterative methods and a starting value. I am trying to see if I can transform it into a linear system and then use a direct linear solver without an initial value.
Sep
4
comment Transforming a nonlinear system to a linear system
Not quite what I was looking for. I don't want to solve the 3x3 system using exact arithmetic. I want to change the nonlinear system to a linear 3x3 system so that I can use a numerically stable direct linear solver. This method is unstable if any of the $y_i$'s are too close or too far apart. +1 for solving the Lorentzian system though. Thanks.
Sep
4
asked Transforming a nonlinear system to a linear system
Aug
30
reviewed Close Linear Transformation $T-T^2=I$
Aug
30
reviewed Close Caratheodory: Motivation
Jul
16
comment How to fill in these steps to evaluate this Gaussian integral?
Cool, thanks. I'll keep playing with this and see if I can use this to get the general case.
Jul
13
revised How to fill in these steps to evaluate this Gaussian integral?
added 276 characters in body
Jul
13
comment How to fill in these steps to evaluate this Gaussian integral?
I know for $\mu=0$, the sum is zero. But how can we get the expression even for $\mu=0$?
Jul
13
asked How to fill in these steps to evaluate this Gaussian integral?