# Tagged Questions

32 views

### How to find max and min bounds of a uncertain function

First I would like to say that I have searched the for uncertain fitting, robust fitting, linear optimization, convex optimization, etc. But I'm lacking the knowledge to solve this problem, and I need ...
24 views

### Spatial Basis Functions…any practical hints on choosing them?

I am not coming from a pure mathematical background, and now in my daily life as an engineering student, I am getting faced to spatial basis functions to approximates variables. The problem is: Are ...
25 views

### Approximate $d\sqrt{x}$ or $d\log(x)$ by a function of the form $a/(1 + bx^c)$

I have some functions of $x$, in the form of $d\sqrt{x}$ or $d\log(x)$ where d is known. I would like to rewrite (approximate is fine) them in the form $\dfrac{a}{1 + bx^c}$, where a, b and c are ...
34 views

### Can we approximate $f(x) = \chi_{(0,\infty)}(x)$ by smooth monotone functions?

Given $f(x) = \text{sign}^+(x) = \chi_{(0,\infty)}(x)$, is it possible to a sequence $f_n$ such that $f_n$ is smooth, $f_n' \geq 0$ and $$f_n \to f?$$ In some sense of convergence? Preferably ...
131 views

### How can I get a good estimation of the following function

The function is $$f(n) = \sum_{i=1}^{n} \frac{1}{2i-1}$$ How can I compute for example $f(20)$ or $f(50)$ without using a calculator. I want to have an approximation
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### Help needed - Approximating functions with geometric integration and derivation

I've somehow managed to approximate some functions using cheap tricks as geometrically derivating the function and then geometrically integrating an easier equivalent of the derivative (see here for ...
30 views

### Approximate function algorithm using a polynomial and Boor splines

I have a defined function and a set of points with equal distance between them. The problem is that I have to approximate the graphic of that function using a polynomial function of 3rd degree and a ...
86 views

### Minimum Argument Difference to Make the Lower Bound > the Upper Bound

Assume $g$ is a function that grows asymptotically as $$g(n) \in\frac n {log(n)} + O(\sqrt n),\,n \in \Bbb N\tag1$$ I wish to find $h(n)$ such that $$g(n) \le g(n+h(n)).$$ i.e. Given the bounds ...
73 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 ...
122 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 ...
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### 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 ...
71 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 ...
188 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 ...
72 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.
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### 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 ...
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 ...
48 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:
44 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 ...
204 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 ...
188 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 ...
51 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 ...
3k 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 ...
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### 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 ...
132 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.
118 views