# Questions tagged [numerical-analysis]

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### Sparse Matrix inversion without actual inversion

I want to know what are the efficient way to invert a Sparse Matrix? Are there any algorithm,linear algebra or expansions that make this task easier with out actually inverting the matrix? Thank you ...
26 views

### Construct unitary $Q$ such that $span\{q_1,q_2\} = span\{v_1,v_2\}$ where $v_1,v_2 \in \mathbb{R}^n$ are given as input

Assume also that $v_1,v_2$ are linearly independent, and $q_i \in \mathbb{R}^n$ denotes the $i$-th column of $Q$. This is what I've got so far. First obtain unit vectors $w_1,w_2$ which are orthogonal ...
154 views

### predictor/corrector and gear integration for positive and negative time steps

I have a predictor method that takes differential equations for 214 biological species and integrates them in time using positive time steps. Right now it is able to successfully integrate the ...
9 views

### Sparse Recovery and Feature Selection

This may be a silly question but are sparse recovery and feature selection problems fundamentally the same? Namely, say we have a set $N$ of features and $S \subset N$ which are the "important&...
84 views

### How to determine the set of real numbers corresponding to a given floating point number?

Let's say we consider IEEE 754 double precision floating-point numbers, and we use RNTE - Round To Nearest, Ties to Even - rounding. I know that the RNTE rounding works this way: given two consecutive ...
97 views

### Numerical Approximation in Java

I am trying to solve an equation which I believe cannot be done analytically, but can use a numerical approximation to get a result. The equation is: \frac{2*\sqrt{\pi}*h*s*e^{m^{2}/(2*s^2)}}{\sqrt{...
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### Computational cost of using dictionary in floating point opertations

I would like to know the computational cost of using/accessing a dictionary. This should depend on the length of the dictionary. Say a dictionary $D$ has $n$ elements. What would be the cost of ...
77 views

### Naviers Stokes equation and machine learning

I am looking for a reference explaining how to solve Navier-Stokes numerically using Machine learning algorithms . Thank you in advance for your help .
I am writing a function that can be split into cases (1)$f(x) \leq f(y)$ and $f(x) \geq f(y)$ or into cases (2)$f(x) < f(y), f(x) = f(y), f(x) > f(y)$ If I have f(x) = f(y), it is ...