Arbitrary-Precision MatricesMathematica arbitrary-precision computations support a form of arithmetic known as significance arithmetic. The fundamental idea of significance arithmetic is that a number is seen as an approximation with an error specified by its precision. When a number is used in a computation the precision of the result may be different according to the properties of the function. For example, here is a number with 30 digits of precision. In[1]:=  |
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Now compute the value of the Sin function for this number. In[2]:=  |
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The result is seen to be less than 30 digits. In[3]:=  |
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In Mathematica, linear algebra computations generally do not use significance arithmetic. They are carried out in what is known as fixed precision, where computations are done with fixed numbers of digits with no attempt to track the error in individual operations. Error tracking is done on an algorithmic level, issuing warnings, for example, when the solution of a linear system may not be correct. In[4]:=  |
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The inverse matrix that is computed consists entirely of numbers with precision of 20. In[6]:=  |
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