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Multiplier -> coefficient

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Antti H S Laaksonen 2017-02-11 00:24:04 +02:00
parent 0f9c46a48d
commit 93e2263475
1 changed files with 3 additions and 3 deletions
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luku23.tex
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@ -329,7 +329,7 @@ The cofactor is calculated using the formula
\[C[i,j] = (-1)^{i+j} \det(M[i,j]),\] \[C[i,j] = (-1)^{i+j} \det(M[i,j]),\]
where $M[i,j]$ is obtained by removing where $M[i,j]$ is obtained by removing
row $i$ and column $j$ from $A$. row $i$ and column $j$ from $A$.
Due to the multiplier $(-1)^{i+j}$ in the cofactor, Due to the coefficient $(-1)^{i+j}$ in the cofactor,
every other determinant is positive every other determinant is positive
and negative. and negative.
For example, For example,
@ -425,7 +425,7 @@ $f(0),f(1),\ldots,f(k-1)$
and the larger values and the larger values
are calculated recursively using the formula are calculated recursively using the formula
\[f(n) = c_1 f(n-1) + c_2 f(n-2) + \ldots + c_k f (n-k),\] \[f(n) = c_1 f(n-1) + c_2 f(n-2) + \ldots + c_k f (n-k),\]
where $c_1,c_2,\ldots,c_k$ are constant multipliers. where $c_1,c_2,\ldots,c_k$ are constant coefficients.
We can use dynamic programming to calculate We can use dynamic programming to calculate
any value of $f(n)$ in $O(kn)$ time by calculating any value of $f(n)$ in $O(kn)$ time by calculating
@ -577,7 +577,7 @@ In the first $k-1$ rows, each element is 0
except that one element is 1. except that one element is 1.
These rows replace $f(i)$ with $f(i+1)$, These rows replace $f(i)$ with $f(i+1)$,
$f(i+1)$ with $f(i+2)$, etc. $f(i+1)$ with $f(i+2)$, etc.
The last row contains the multipliers of the recurrence The last row contains the coefficients of the recurrence
to calculate the new value $f(i+k)$. to calculate the new value $f(i+k)$.
\begin{samepage} \begin{samepage}