Matlab basic - how to get around floating point?

[catsarebad]

i'm trying to learn MATLAB and as such i stumbled here while looking something up

http://www.mathworks.com/help/matlab/matlab_prog/floating-point-numbers.html

so the questions is

how does someone avoid something like

e = 1 - 3*(4/3 - 1) (this is example 1 in the webpage above)

not being zero

or this not being zero

sin(pi) (this is in example 1 again)


or this being zero
sqrt(1e-16 + 1) - 1 (in example 2)

thank you very much!

 

[marcusl]

Matlab is a numerical solver. If having a result like 1e-16 is not close enough to zero for you, you can increase the numerical accuracy that Matlab provides, at the cost of slowing computations down. If you really want exactly zero, use a symbolic calculation code like Mathematica or Maple. They do algebraic manipulations and evaluations the way you would do them in school.

 

[AlephZero]

Did you read the reference on that web page? http://www.mathworks.com/company/newsletters/news_notes/pdf/Fall96Cleve.pdf
Another (longer) explanation of floating point arithmetic: http://web.cse.msu.edu/~cse320/Documents/FloatingPoint.pdf

 

[FactChecker]

This is a common problem. Just don't program any logic decisions based on equality of two real numbers. Always allow some tolerance when comparing two reals and apply the tolerance so that the safe decision will be made if the reals are within the tolerance.

 

[alphy]

I understand the importance of accuracy and precision in numerical calculations. Floating point numbers in MATLAB can sometimes lead to unexpected results due to the limitations of computer hardware. To avoid these issues, there are a few strategies that can be implemented:

1. Use the "format" function to change the display format of numbers. This can help to see the actual value of a number rather than its rounded version.

2. Use the "eps" function to determine the smallest number that can be represented in MATLAB. This can help in setting a threshold for when a number should be considered as zero.

3. Use the "round" function to round numbers to a certain number of decimal places. This can help in reducing the effects of rounding errors.

4. Use the "sym" function to work with symbolic variables instead of floating point numbers. This can help to avoid any precision issues.

5. Use the "vpa" function to increase the precision of calculations. This can be helpful in cases where high precision is required.

It is also important to note that some mathematical operations, such as division and square root, can introduce errors in floating point calculations. Therefore, it is important to understand the limitations of the hardware and the algorithms being used, and to choose appropriate methods for each specific case.