# Questions tagged [approximation]

A method of finding nearly-optimal solutions to a problem. Generally, this terminology is applied to algorithms and heuristics for solving NP-Hard problems in computer science.

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### Drawbacks of Newton-Raphson approximation with approximate numerical derivative

Suppose I have some function $f$ and I want to find $x$ such that $f(x)\approx 0$. I might use the Newton-Raphson method. But this requires that I know the derivative function $f'(x)$. An analytic ...
4answers
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### Can the solution of a linear system of equations be approximated for only the first few variables?

I have a linear system of equations of size mxm, where m is large. However, the variables that I'm interested in are just the first n variables (n is small compared to m). Is there a way I can ...
6answers
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### Approximate spectrum of a large matrix

I want to compute the spectrum (all the eigenvalues) of a large sparse matrix (hundreds of thousands of rows). This is hard. I am willing to settle for an approximation. Are there approximation ...
1answer
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### The Remez Algorithm

The Remez algorithm is a well-known iterative routine to approximate a function by a polynomial in the minimax norm. But, as Nick Trefethen  says about it: Most of these [implementations] go ...
1answer
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### Efficient solution of mixed integer linear programs

Many important problems can be expressed as a mixed integer linear program. Unfortunately computing the optimal solution to this class of problems is NP-Complete. Luckily there are approximation ...
1answer
981 views

### Numerical methods for inverting integral transforms?

I'm trying to numerically invert the following integral transform: $$F(y) = \int_{0}^{\infty} y\exp{\left[-\frac{1}{2}(y^2 + x^2)\right]} I_0\left(xy\right)f(x)\;\mathrm{d}x$$ So for a given $F(y)$ ...
1answer
191 views

### Efficient Gravitational Field Implementation

I asked a similar question on physics.stackexchange, being ignorant about this website. I am basically looking for an efficient way to implement gravitational fields. I have a huge 2D space, with ...
1answer
795 views

### Polynomial Fitting from Chebyshev Coefficients

I have been reading Numerical recipes about how to create a power series approximation to a function once you have a Chebyshev approximation to the function. However it is still very unclear to me how ...
3answers
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1answer
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### Efficiency of an algorithm

I designed an algorithm to find the global minimum of a function and implemented it in MATLAB. And I also implemented the "Tunneling algorithm" for the global minimum of a function in MATLAB. But now,...
2answers
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### Methods for fast approximation of convolution

What are the state of the art methods for fast 2D convolution approximation? I'm familiar with SVD based multiplication and cross approximation approaches, but would be thankful to get additional ...
3answers
144 views

### What are some algorithms to calculate the width of an arbitrary polygon when a bounding box approximation is inaccurate

What are some alternative algorithms to creating a bounding box for finding the max width of a concave, simple winding polygon, like the one in the below image? I prefer solutions that are more ...
2answers
946 views

### How to detect key turning points on a driven road?

I am looking for a description of algorithm which allows me to detect key turning points on the road amongs a set of all given points. I've ilustrated my problem on the below image: Green spots: ...
1answer
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