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8
votes
1answer
314 views

Confused by (apparent) inconsistent precision

$$ e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925 $$ E^(Pi Sqrt[163.0]) N[E^(Pi Sqrt[163.0]), 35] NumberForm[E^(Pi Sqrt[163.]), 35] returns ...
45
votes
2answers
2k views

When I can assume that all decimal digits returned by Mathematica are provably correct?

How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: ...
5
votes
1answer
577 views

ReadList can't read from file containing high-precision Reals

I want to read a file which contains seven columns of real numbers. Mathematica seems to have a problem with the high precision I need. My code: ...
6
votes
2answers
2k views

How to convert a string of number into real numbers without precision loss

I searched and did not find similar answers which can resolve the 'no precision loss' issue. A sample string is: ...
16
votes
0answers
192 views

Is MathieuC for moderately large imaginary arguments broken?

I'm trying to plot MathieuC[-3,0.3,I x] for $x\in[0,10]$, and here's what I get even with arbitrary precision arithmetic (here I use ...
6
votes
2answers
296 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
8
votes
2answers
698 views

Finding differences between Pi with varying number of decimals

I have the following code In[32]:= N[Pi, 2] Out[32]= 3.1 In[33]:= N[Pi, 1] Out[33]= 3. In[34]:= N[Pi, 2] - N[Pi, 1] Out[34]= 0.*10^-1 Why can't Mathematica ...
3
votes
1answer
196 views

Fixed-Point Numbers in Mathematica

I am working with a library that needs input in a Fixed Point notation. I’d like to figure out a way to convert the floating point results into fixed point representation. The fixed point length is ...
2
votes
2answers
183 views

Permanently rounding numbers/values to a given number of significant figures

I am searching for a simple way of rounding and setting an input to a desired number of significant figures. There are a vast number of posts that discuss similar problems, but none address this ...
1
vote
1answer
230 views

Output precision

I've solved some equations using FindRoot and then computed some values. Now when I print the output, I only get a certain precision {{0.01, 496.983, 61.3147, ...
0
votes
1answer
149 views

How can I obtain more significant digits? [duplicate]

I type f1[x_] := 12 x^5 - 975 x^4 + 28000 x^3 - 345000 x^2 + 1800000 x N[f1[15.5], 15] and obtain 3.74112*10^6 BUT It´s not true!!! the result is larger than ...
3
votes
4answers
197 views

AccountingForm w/o significant figures

Basically I want to build a chart like something I would do in Excel. It should look like this: Here is the formula I'm using and what I've done so far ...
13
votes
2answers
376 views

Why do NumberForm and Round apparently use different tie-breaking methods?

When rounding numbers (for example, rounding a real number to the nearest integer), the "round to nearest" rule is usually used. For example, 1.4 is rounded down to 1 and 1.6 is rounded up to 2. ...
8
votes
2answers
206 views

Error computing sum of sum of digits

I've defined a function that computes the sum of the base-b digits of n: DigitSum[n_, b_] := Total[IntegerDigits[n, b]] Then I defined a function that computes ...
6
votes
2answers
311 views

A problem about fixed point iteration theory

Description Recently, I have been learning a couse called "Numerical Analysis". The fixed point iteration theory was introducted to solve the ...
6
votes
3answers
269 views
6
votes
1answer
173 views

Numerical error in Mathieu functions

Consider the MathieuCharacteristicA function, which is a piecewise function according to the documentation. The discontinuity happens at integer number. ...
4
votes
3answers
229 views

Increasing the precision of a calculation

Clearly I have misunderstood how to do this: I seem unable to understand how to get more digits out of a calculation and I can't see why - the following piece of code illustrates the issue. ...
4
votes
1answer
108 views

Issues with $MachineEpsilon

I'm attempting to add $MachineEpsilon to numbers I am pulling from the domains of 3 interpolating functions. I pulled 3 numbers, and for one of these numbers adding ...
4
votes
1answer
168 views

Padding plot ticks with zeros on the right

I would like to know how can I make a real-valued plot tick pad with a zero to the right of the decimal point on integer values. This is what I have: ...
3
votes
2answers
153 views

Explicit digit-count (precision) of real number

I'm trying to do something which seems like it should be simpler than it is (at least in my attempts at it). I have some code where I read in a list of numbers generated for me by a coworker. These ...
3
votes
1answer
46 views

Deferent results depending on the input form of the matrix [closed]

Why is it so, N[Eigenvectors[{{1., 0.5, 4.}, {2., 1., 2.}, {0.25, 0.5, 1.}}]] returns: ...
0
votes
0answers
44 views

CharacteristicPolynomial returns 0

I have the following matrix. ...
0
votes
2answers
71 views

Why is Sin[2.0 Pi] = -2.44929 x 10^-16 and not 0.0?

Why does Sin[2.0 Pi] evaluate to -2.44929 x 10^-16 and not 0.0?