# 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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### Improving function approximation with neural network

I am building a neural network to approximate a data set which takes 3 inputs and gives 1 output. After testing the network using a few different iterations of hidden layers and adjusting optimizers ...
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### Boundary conditions for an FEM approximation of the Laplace operator

Using FEM, I want to approximate the Laplacian $$u = \nabla \cdot \nabla h \, ,$$ where $h(x,y)$ is an FEM approximated scalar field on the same mesh, i.e. piecewise differentiable. I am using MOOSE ...
131 views

### Floating point and global error in Euler Method

Inspired by this answer, I tried to understand when floating point errors come into visibility and to check it also comparing the plot of the numerical solution with Explicit Euler with the analytical ...
71 views

### Is there a source/cookbook of equations that approximate geometric shapes?

I'm numerically modelling flows around various geometric 2D shapes. Is there a good source/cookbook of equations that approximate these? Some examples are Rectangle: $(x-a)^n+(y-b)^n < r^n$ where ...
53 views

### Continuous limit and nonlinear functional analysis

I have a kind of general question about approximation schemes in nonlinear functional analysis. Given a nonlinear map $\Phi$ from an open set (in an infinite dimensional Banach space) of functions to ...
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### Error curve does not oscillate in between reference points using Remez

Using the Remez algorithm, implemented using multi-precision library, in certain functions that I want to approximate, the error curve does not oscillate in between reference points, and so no roots ...
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### Fast approximate solver for vehicle routing problem

I need to solve capacitated asymmetrical vehicle routing problem with time windows on ~30k points. Time limits for calculations are 2 hours. I've tried using Clarke and Wright savings algorithm, it is ...
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### Derivatives of a Chebychev polynomial

I am using Chebychev collocation nodes for approximation, and my problem requires me to calculate derivatives of the polynomial. I have been reading from a few sources, but I am not sure I understand ...
57 views

### Computing dilogarithm

I'm measuring the integral of a quantity which, mathematically, requires the computation of a dilogarithm function. $$\operatorname{Li}_2(be^{ax})$$ where $b$ and $a$ (are real and) can be positive ...
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### Fast algorithm for computing matrix square root using randomized linear algebra?

Is there a fast algorithm for computing the matrix square root of a real symmetric matrix using random matrices or randomized algorithms?
372 views

### Matching/Assignment Problem

I'm not sure how I can represent and solve the following problem. I have a list of sales (timestamp and quantity) and a list of corresponding inventory draws (timestamp and quantity). What I ...
421 views

### 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,...
Let $D_{\nu}(.)$ is the parabolic cylinder function (http://mathworld.wolfram.com/ParabolicCylinderFunction.html) And $\Gamma(.)$ is the Gamma function. Define \$s_y(\mu,\nu,t,z)=2^{\nu}\...