# Questions tagged [numerical-analysis]

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• 101
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### How to test for overflow when multiplying floats

I am trying to implement a 3-term recurrence relation: $$p_{n+1} = ap_n + bp_{n-1}$$ This can be implemented as ...
• 208
1 vote
99 views

### Why do I get different results from two calculation methods?

I am wondering what the reason for the following is We know that , exponential has a taylor representation : $$exp(x)=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+...$$ Using the first n terms , in R , ...
• 113
1 vote
133 views

### Real RAM computational mode

Given a real value $M>0$, I want to compute the greatest value of $\epsilon$ strictly smaller than $M$. Given the assumption that the computational model is Real-RAM, how to find a real number ...
1 vote
49 views

• 123
1 vote
75 views

### 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 ...
• 11
568 views

### Big O notation: removing big O from denominator

In A First Course in the Numerical Analysis of Differential Equations (page 26) Arieh Iserles gives the following derivation: \frac{\rho(w)}{\ln(w)}=\frac{\xi+\xi^2}{\xi-\frac{1}{2}\...
1 vote
28 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 ...
• 111
387 views

### Understanding truncation and rounding error in IEEE floating point system?

I'm trying to understand the theory behind finding the optimal $h$ value for differentiation in this definition: $$\frac{f(x+h) - f(x)}{h}$$ as $h$ tends to 0. Here is my understanding: ...
• 155
1 vote
145 views

### Float type variable uncertainty

I developed an image processing software and I need to do a numerical analysis of it, considering the error propagation associated to its operations and the uncertainty of float type variables caused ...
55 views

### 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 ...
• 1
96 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 .
1 vote
62 views

### What is a logical approach to developing an algorithm which can find the optimal parameters for a function which make it best fit a given data set?

Consider the highlighted columns in the following table: Starting with 100,000 newborns, $l_{x+2}$ denotes the number of individuals in the sample still alive at age $x+2$. If we consider Makeham's ...
• 467
976 views

### Reception of numerical infinities

A group of computer scientists associated with numerical analyst Yaroslav Sergeyev have published numerous publications recently on a scheme proposed by Sergeyev that uses terms like Infinity Computer,...
22 views

### Numerical analysis - f(x) = f(y)

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 ...
• 121