# 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 ...
149 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 ...
69 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 ...
82 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 ...
68 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 ...