Create a 4-by-4 matrix.
format short X = hilb(4)
X = 1.0000 0.5000 0.3333 0.2500 0.5000 0.3333 0.2500 0.2000 0.3333 0.2500 0.2000 0.1667 0.2500 0.2000 0.1667 0.1429
View the rational representation of the matrix using
rats. The result is the same as using
R = rats(X)
R = 1 1/2 1/3 1/4 1/2 1/3 1/4 1/5 1/3 1/4 1/5 1/6 1/4 1/5 1/6 1/7
Find the rational representation of
pi with the default character vector length and approximation tolerance. The result is the same as using
ans = 355/113
Adjust the length of the output, which also adjusts the approximation tolerance.
ans = 104348/33215
The resulting rational approximation has greater accuracy. As the output length increases, the tolerance decreases.
Adjust the output length again to achieve greater accuracy.
ans = 1146408/364913
The resulting approximation agrees with
pi to 10 decimal places.
X— Input array
Input array, specified as a numeric array of class
Complex Number Support: Yes
strlen— Length of character vector
Length of character vector, specified as a positive integer. The default length is 13, which allows for 6 elements in 78 spaces.
S— Rational output
Rational output, returned as a character vector.
rats obtains rational approximations with
= rat(X,tol), where
Thus, the tolerance is inversely proportional to the output length,