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# Questions tagged [numerical-algorithms]

Questions related to algorithms that use numerical approximations for the problems of mathematical analysis.

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### Robust two lines/segments intersection point in 2D

Given two line segments the problem is to find an intersection point of corresponding lines (assuming that they are not parallel or coincide). There is a Wikipedia article which gives us exact ...
18 views

### Algorithm to position samples minimizing error

We have a 1D function f(x). We would like to approximate this function with a polyline of n points. How can we find the ...
6 views

### Efficiently populate a look-up table for a function over a range of arguments

I am minimizing a scalar function $f$ which takes a $n$-dimensional vector input and outputs a scalar value. I have code that given an input $x$ will compute the output of $f(x)$ (a scalar), its ...
17 views

### Are there practical usage of determinants in numerical simulation?

I know the historical importance of the link between linear systems and determinants. I also know that determinants have a beautiful connection with non-singular matrices, i.e., if a matrix is non-...
61 views

### Computing an Expression

I am writing code to evaluate the following expression: $$\frac{(a+b+c)!}{a! b! c!}$$ where $a$, $b$ and $c$ are on the range of $10$ to $500$. The result is going to be a floating point number. ...
193 views

### Is order of matrix multiplication affecting numerical accuracy of the result?

I have to multiply three matrices of floats: A (100x8000), B (8000x27) and C (27x1). Is ...
83 views

### How to find i-th root of n whose remainder is the smallest?

Given a number n, what is the most assymptotically fast algorithm to express it in terms of base^exponent + rem such that rem is the smallest possible and base is limited from 2 to some relatively ...
37 views

### Search for numerical solutions of underdetermined systems of quadratic equations

I'm looking for an algorithm that can quickly generate an approximate real number solutions of an underdetermined quadratic system. My task is to explore its algebraic variety. I'm interested in a ...
49 views

### Efficient algorithm for numerical estimation of 3D rotation matrix

I am writing a computer vision related program and stuck on a problem. I have a system of quadratic equations where M is a constant 3x3 matrix, is the 3x3 identity matrix, and we are solving for the ...
26 views

### When an algorithm says Summation this, and Integral that, what does it mean in coding terms?

I'm a student at a college with only two units of mathematics and I don't know if I'm asking in the right place so please bear with me. I'm currently reading GPU Gems by nvidia and I have a question....
26 views

### Rigorous error bounds for eigenvalue solvers

I computed the first four eigenvalues of a quite large ($2^{24}\times 2^{24}$) but very sparse matrix. I used pythons in-build function sparse.linalg.eigsh to compute them. I need a validation that ...