Questions tagged [extrapolation]
For question on extrapolation, the process of estimating, beyond the original observation interval.
134 questions
1
vote
0
answers
63
views
Richardson Extrapolation to the highest possible accuracy to evaluate a function derivative
I am given f(x)=cosh(x) and asked to estimate f’(0.6) using Richardson Extrapolation to the highest possible accuracy. I computed the centered difference using h1=0.2 and h2=h1/2=0.1
I got
D(0.1)=0....
- 11
0
votes
0
answers
54
views
What is the benefit of the force of mortality over PDF in lifetime analysis
What is the benefit of using the force of mortality $μ_x$ instead of the Probability Distribution Function $f_x(t)$ of a lifetime random variable $T_x$?
I understand that if I have the continuous ...
0
votes
1
answer
80
views
Error terms in the Richardson extrapolation.
The details of what is happening are not important the question I have. We have a solution $X_t(\omega)$ to a stochastic differential equation and an approximation with step size $N$ denoted $Y_t^N(\...
- 1,568
2
votes
0
answers
64
views
Blending of two functions such that the same prescription also holds for their derivatives
Prologue: It's easy to blend one real function $f(x)$ into another, say $g(x)$, by considering a convex combination with a transition function $\eta(x)$,
$$
h(x) = (1-\eta(x)) f(x) + \eta(x) g(x)
$$
...
- 2,270
1
vote
1
answer
91
views
Schauder bases and embeddings in Hilbert spaces
I would like to know whether continously and densely embedded orthonormal bases are always Schauder bases of the larger space. More precisely:
Let $(H, \langle \cdot,\cdot\rangle_H)$ and $(\tilde{H}, \...
- 279
1
vote
1
answer
220
views
Does Richardson Extrapolation do anything else than increasing the speed of convergence?
I feel like I am conceptually confused about the point of Richardson Extrapolation. How I understood it, is that if we have some function $\mathcal{A}(h)$ that approximates $\alpha_0$, and can be ...
- 11
0
votes
1
answer
47
views
Prove boundary of error when extrapolating origin of function
Given are $n \in \mathbb N, h > 0$ and $a \in C^{n+1}(0, h)$. Furthermore, let $(x_k)_{k = 0, \dots, n}$ be a monotonic decreasing sequence of positive numbers with: $$x_0 \leq h \;\;\; \text{ and }...
- 379
1
vote
1
answer
421
views
How do I calculate the expected number of duplicates in a set based on the number of duplicates found only in a sample? [closed]
I have a set of 10,000 points of data. I know that some of those points of data are identical to other points of data (i.e. duplicates), but (for now) there are no triplicates, quadruplets, etc. This ...
- 11
2
votes
0
answers
64
views
$[1]$ Does good $R^2$ necessarily tells us that the experiment went right? $[2]$ Is not extrapolation dangerous when used for a far point?
In an experiment, the relation between $x$ and $y$ is linear.
$x_\text{actual} = \alpha_x x_\text{observed} + \beta_x + \gamma_x$. [Here, $\alpha$ is the slope, $\beta$ is the intercept, and $\gamma$ ...
- 5,894
0
votes
0
answers
141
views
Error of Richardson Extrapolation with composite midpoint rule
My goal is to find an (exact) error expression for Richardson extrapolation applied to the composite midpoint rule. I know that the error for this rule is $$\displaystyle\frac{(b-a)h^2}{6}f^{''}(\xi)$$...
user948998
0
votes
0
answers
75
views
Is there a general form of a logical formula with N variables?
Let N = 2. Then there are 16 possible non-equivalent N variable logical formulas, listed below.
False,
A ∧ B,
¬(A → B),
A,
¬(B → A),
B,
A ⊕ B,
A v B,
¬(A v B),
¬(A ⊕ B),
¬B,
B → A,
¬A,
A → B,
¬(A ∧ B),...
- 99
0
votes
0
answers
44
views
Testing linear extrapolation for validity
How can we assess the validity of a linear extrapolation? Is there a standard way of measuring the soundness of an extrapolation, like "statistical significance"?
The only way I can think of ...
- 465
0
votes
0
answers
106
views
What "tool" to extrapolate traffic data on graph used for routing (Open Street Maps).
Background (non-math):
I'm planning to use Open Street Maps data to find the fastest route by car between points. Data is a directed graph where vertices represent locations, and edges are routes. ...
2
votes
1
answer
73
views
How to create synthetic data for a decaying curve in order to extrapolate it beyond some point? [closed]
In the following curve , I would like to extend the measurements beyond $x$=1 in order to have a better estimate of the green curve compared to red line.
Note: I do not have the analytical form of the ...
- 23
1
vote
0
answers
97
views
How do I extrapolate probability distributions from a single distribution?
If I have 3 fair 6 sided dice, and 1 throw consists of rolling all 3 of them, how do I extrapolate the distribution of roll values of each individual die for a specific sum from the distribution of ...
- 11