2
votes
2answers
65 views

$C^\infty$ approximations of $f(r) = |r|^{m-1}r$

Consider $f(r) = |r|^{m-1}r$ where $m \geq 1$. Is it possible to find $C^\infty$ functions $f_n$, such that $f_n \to f$ uniformly on compact subsets of $\mathbb{R}$, $f_n' \to f'$ uniformly on ...
3
votes
2answers
87 views

Approximate $|x|$ with a smooth function

I am trying to get the derivative of $|x|$, and I want that derivative function, say $g(x)$, to be a function of x. So it really needs the |x| to be smooth (ex. $x^2$); I am wondering what is the ...
0
votes
0answers
19 views

Padé approximant of transfer function with gain and time delay.

$$ H(\omega) = A e^{-j \omega \tau} $$ I'm trying to use Padé approximation to generate a numerator and denominator polynomial for the above transfer function but genuinely struggling with how to ...
1
vote
0answers
27 views

Best Fit Curve and Function for 4D Data?

I have experimental data of 4 dimensions, and I want to computer-generate an approximated function from that. If it helps to clarify, I'm testing a pendulum's period based on variable length, starting ...
3
votes
4answers
166 views

Using $(1+x)^k \approx 1+kx$ to approximate?

Use the approximation $(1+x)^k \approx 1+kx$ to estimate $(1.0003)^{26}$ and $\sqrt[4]{1.006}$. I know how to solve this step-by-step, but I don't understand what I'm doing exactly: why does ...
2
votes
1answer
51 views

show that any continuous function can be approximated uniformly

I do not know where to start because i have not dealt with a question like this before. I feel that i have to use the Stone-Weierstrass theorem, but im not sure how to use it.
3
votes
0answers
77 views

Representation for a function that, when added/multiplied/composed with another function of the same form, yields a new function of the same form

I apologize for the possibly unclear wording of the title. I'm not well versed in math terminology. I'm after a concrete representation of a function, eg $y(x) = Ax^p$ (where $A$ and $p$ are ...
1
vote
1answer
56 views

Approximating a function

I'm sorry if this question in not well formed... I would like to perform a computation of the following function: f() = -2*X1 -1*X2 +0*X3 + 1*X4 +2*X5 (The ...
0
votes
1answer
46 views

Best way to approximate function

What is the best approximation for function like on attached image ? Function is increasing or decreasing from "spike" to "spike" Zoom to the first few members: All members:
2
votes
1answer
42 views

determining sign of function containing logarithm.

I would like to know the sign of the following term in general. I tried approximately and it was negative. Is there any $m_0$ such that for all $n>m>m_0$, the following function is positive or ...
0
votes
0answers
191 views

Approximate a complicated mystery function

Let there exist a mystery function ƒ. ƒ accepts exactly 2 arguments, A & B. As B approaches A, ƒ approaches A, at a simple exponential growth rate E. As B approaches 0, ƒ approaches the mean ...
1
vote
1answer
163 views

approximating a discrete function with a continuous one

Let $f:[0,1]\rightarrow \mathbb{R}$ be a continuously differentiable function that reaches a global maximum at $x^*\in(0,1)$. Now, consider its 'discrete' counterpart. That is, consider the collection ...
-1
votes
2answers
49 views

Aprroximate graph to function

there is a set of points which set a graph that is not linear. Is there any method to approximate a function that is close enough to this graph? I've read some articles and got to know approximation ...
2
votes
3answers
2k views

Software to find a function for data approximation

I've got some y(x) 2D data set. I would like to find a function fitting this data: Is there any open source or free software to find a function to approximate a data sequence like the above? Here ...
2
votes
1answer
68 views

If f is in LipK[a, b], show that f can be uniformly approximated by polynomials in LipK[ a, b].

Question: If f $\in$ LipK[a, b], show that f can be uniformly approximated by polynomials in LipK[ a, b]. Context: f $\in$ LipK[a,b] then it is Lipschitz with constant K. The text I am currently ...
2
votes
1answer
120 views

Upper bound for $\Gamma(x+y)$

Let $x, y \geq 1$ be two real numbers. I am wondering if one can get an upper bound for $\Gamma(x+y)$ in terms of $\Gamma(x)\Gamma(y)$? Any references or ideas are very appreciated. Thank you.
0
votes
1answer
116 views

Approximation of function on interval

I'm looking for an accurate but as simple as possible approximation of $S(x,\lambda) = \frac{1}{(1-x) [x-(1-\lambda )]}\left((1+\lambda ) \left(\frac{x(1+\lambda)}{1-\lambda ...
1
vote
5answers
476 views

Find square root approximation function (tool)

first I have to apologize for any uncorrect naming or categorisation of my question, as I am an electrical engineer rather than a mathematican. I try to find a simple solution for my problem: I have ...
1
vote
0answers
115 views

Efficient way to recompute weights when shifting range of Legendre polynomial bases

I am storing a 2D (Cartesian) density function as a 2D patch with known X/Y limits and a set of 11 coefficients of the third order 2D Legendre polynomial basis functions over that patch. This works ...
3
votes
2answers
213 views

Multidimensional Interpolation within a polygon

Apologies in advance if I get terminologies wrong (not sure if "multidimensional interpolation" is the right term), I'm not really that great at maths, but here goes: Suppose we have two 2D points, ...
4
votes
3answers
476 views

How to find a Newton-like approximation for that function?

I want to find the complex fixpoint $t=b^t $ for real bases $b> \eta = \exp(\exp(-1))$. added remark: I'm aware that there is a solution using branches of the Lambert-W-function, but I've no ...
0
votes
1answer
175 views

Restoring the function by its graph

I need a function that will produce a graph similar to the one below. This function is odd, symmetrical relatively to origin in III quarter. A is an asymptote (the top part is similar to ...
0
votes
1answer
142 views

Taylor Series. Reusing an approximation of a function

I have this function, $e^{-x}$ bounded between 0 and 1500 and I have an approximation by Taylor Series of the same function bounded between 0 and 0.5. I would like to express my function $e^{-x}$ ...
0
votes
1answer
99 views

Development of a specific hardware architecture for a particular algorithm. Modelling fuctions by Taylor sSeries.

I'm trying to develop a architecture hardware to make a implementation of an algorithm that can be descompose in terms of sums, multiplications, subtractions and exponential functions. I'm trying to ...
5
votes
3answers
3k views

Find formula from values

Is there any "algorithm" or steps to follow to get a formula from a table of values. Example: Using this values: ...