taylor series and vector/matrix etc

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Vegan

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Feb 26, 2012, 3:42:11 PM2/26/12
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I created a exp function for a matrix, had to first create a pow
function then exp could call that
no problem

so I used a taylor expansion to do the work

so it got me thinking, do vectors and matrices all good with taylor
expansions etc

Rob Beezer

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Feb 27, 2012, 7:46:36 PM2/27/12
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You can form any polynomial of a square matrix, since powers make sense, and
then scalar multiples and addition are the most basic operations. This is
Subsection EE.PM.

With vectors this would not be so natural, but it is sometimes advantageous to
multiply a polynomial of a square matrix times a vector. See the proof of
Theorem EMHE.

Rob

Vegan

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Mar 2, 2012, 8:47:53 AM3/2/12
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Thanks, I was considering something along the line of
exp(A) where A is a matrix etc

template <typename T> matrix<T> pow(matrix<T> &radix, int signficand) {
matrix<T> product = radix;
for (int i = 1; i < significand; i++)  // Brutal computations
product = product * radix;
return product;
}

template <typename T> matrix<T> exp(matrix<T> &exponent) {
matrix<T> sum = 0; // Maclaurin series expansions
for (int k = 0; k < 6; k++) { // 6 terms should be enough
sum = sum + (pow(exponent, k) / factorial(k)); // Power series
}
return sum;
}
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