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Questions tagged [approximation]

For questions that involve concrete approximations, such as finding an approximate value of a number with some precision. For questions that belong to the mathematical area of Approximation Theory, use (approximation-theory).

Approximations are representations of numbers that aren't exact, for example $\sqrt{2}\approx 1.41$. Such representations may be obtained using differentials (more generally, Taylor's formula), linear interpolation, etc.

4607 questions
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least squres vs. lagrange interpolation

can some one tell me the differences between these two approximation techniques, what are the strengths and weaknesses of each, and which better one to use. Thanks
sahar salah eldeen
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How to decompose a result of a multiplication?

I've got a multiplicative-with-noise model $F(x,y)=S(x)*R(y)*D(x,y)+N$, where $S(x)$ and $R(y)$ are unknown functions, $D(x,y)$ is a distance function, that is, a function that depends only on $|x-y|$ and decreases quickly when distance increases.…
mbaitoff
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Angle measurement

Assume I want to compute one of the angles of a right triangle doing $n$ measurements of the sides with a ruler. In order to increase the precision I make several measurements. After that I compute $\tan \theta$ for each of the…
Dmitry Kazakov
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solve for a constant value?

Can we solve for $g$ when $\varepsilon$ is small? $\newcommand{\sinc}{\operatorname{sinc}}$ $$3\sinc\left(-1+ \frac\varepsilon T \right)-3\sinc\left(1+\frac\varepsilon T\right)-\sinc\left(-3+\frac\varepsilon T\right)+\sinc\left(3+\frac\varepsilon…
Elnaz
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Rounding with significant digits

I'm dealing with significant digits right now, and recently I've been having a nagging question in my mind. When we have digits past the last significant digit in a quantity, do we round the last SD by the first non-SD? For example, say we have a…
Jonathan Spirit
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Quadratic approximation of $tan(x)$ at 0.

I have tried this: http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-2-applications-of-differentiation/part-a-approximation-and-curve-sketching/problem-set-3/ and checked my solution of the problem 2A-6. In the…
user50224
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Signifcant Figures -- Why are rules for multiplying and adding true?

I found this other question that deals with this somewhat, but I am still unclear as to why the rules for adding/subtracting and multiplying/dividing significant figures are the way they are. In the linked question above, the response to why…
1110101001
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Curve approximation by some known points on the curve

I want to approximate a curve by some known points on the curve. I can choose these point. My curve is shown as below: I have to use such a equation: f(x) = a1x^1 + a2x^2 + a3x^3 + a4x^4 1) Is it a proper equation for my approximation ? 2)…
Hamed
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I do not quite understand what destructive cancellation is, can someone explain it please?

I have been given this example 2.0013−2.0005=0.0008. The destructive cancellation is the large common value, here the 2, that disappears.
Jed
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How is this method for computing square roots a manifestation of Newton's method?

I discovered that we can use Newton's method to conveniently compute the square root of a positive integer. Newton's method stipulates that we keep iterating as such: $$ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} $$ However, apparently, we can just…
David Faux
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Question about the Weierstrass approximation theorem

By the Weierstrass approximation theorem for $f\in C[a,b]$ there exists a sequence ($Q_n$) of polynomials such that $Q_n(x) \rightrightarrows f(x)$ on $[a,b]$ or equivalently for each $\varepsilon >0$ there exists a polynomial $Q$ such that…
Alex
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Use tangent line to find approximation

$f(x) = x^2 - 3x + 5$, the tangent line to the graph of $f$ at $x = 3$ is used to approximate values of $f(x)$. Which of the following values $3.4$ $3.5$ $3.6$ $3.7$ $3.8$ is the greatest value of x for which the absolute value of the error of…
user140254
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Approximations. Newton's method - composite Simpson's rule

Can you help me please to solve this problems and if you can give me some helpful information. Thanks!
Iuli
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approximation for formula -- relation to exp function

Let $n>0$ be a natural number. I am looking for an M(n) of the following function: $$ f(n) = (1 - n^{-1/4})^n < M(n) $$ I know that if $n$ goes to infinity $f(n)$ goes to $0$. Now, I wonder if there is some simple expression for $M(n)$ that…
Bernd
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Counterexample to smooth approximation of sobolev function on closure of set without $C^1$ boundary

I'm working through the following problem, and I just need a hint to finish it I think. Consider the set $\Omega = B(0,1) \backslash \left\{x\in \mathbb{R}^N : x_N = 0 \right\}$. We are given the function \begin{equation*} u(x):= \left\{…
John
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