- #1
Mathman23
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The following formula [tex]E(a,b) = \sum_{j=1} ^{N} (y_{i} - (a + b_{i})^2[/tex] is used to messure the distance between the points [tex](x_1,y_1),(x_2,y_2), \ldots, (x_n, y_n) \in \mathbb{R}^2 [/tex] and the line [itex]y=a+bx[/itex]
I need to find a set of points [tex](a,b) \in \mathbb{R}^2[/tex] where E(a,b) using tools of linear Algebra.
I'm given the following vectors:
[tex]x = \left [ \begin{array}{c} x_{1} \\ \vdots \\ x_{N} \end{array} \right ], v = \left [ \begin{array}{c} y_{1} \\ \vdots \\ y_{N} \end{array} \right ], \ \ \overline{x} = \frac{1}{N} \sum_{j=1} ^N x_{i}, \ \ \overline{y} = \frac{1}{N} \sum_{j=1} ^N y_{i} [/tex]
I'm tasked with calculating [tex] \mathb{\frac{dE}{da}} , \mathb{\frac{dE}{db}}[/tex] and showing that if [tex] \mathb{\frac{dE}{da}}=0 , \mathb{\frac{dE}{db}}= 0[/tex] leads to the linear system.
[tex]A \left [ \begin{array}{c} a \\ b \end{array} \right ] = c[/tex], where [tex]A = \left [ \begin{array}{cc} \frac{1}{x} \ \ \overline{x} \\ \ \ \frac{x \cdot x}{N} \end{array} \right ][/tex] and [tex] c = \left [ \begin{array}{c} \overline{y} \\ \frac{x \cdot y}{N}\end{array} \right ] [/tex]
Anybody have any hits/idear for to solve this assignment ??
Many thanks in advance
Sincerley Fred
I need to find a set of points [tex](a,b) \in \mathbb{R}^2[/tex] where E(a,b) using tools of linear Algebra.
I'm given the following vectors:
[tex]x = \left [ \begin{array}{c} x_{1} \\ \vdots \\ x_{N} \end{array} \right ], v = \left [ \begin{array}{c} y_{1} \\ \vdots \\ y_{N} \end{array} \right ], \ \ \overline{x} = \frac{1}{N} \sum_{j=1} ^N x_{i}, \ \ \overline{y} = \frac{1}{N} \sum_{j=1} ^N y_{i} [/tex]
I'm tasked with calculating [tex] \mathb{\frac{dE}{da}} , \mathb{\frac{dE}{db}}[/tex] and showing that if [tex] \mathb{\frac{dE}{da}}=0 , \mathb{\frac{dE}{db}}= 0[/tex] leads to the linear system.
[tex]A \left [ \begin{array}{c} a \\ b \end{array} \right ] = c[/tex], where [tex]A = \left [ \begin{array}{cc} \frac{1}{x} \ \ \overline{x} \\ \ \ \frac{x \cdot x}{N} \end{array} \right ][/tex] and [tex] c = \left [ \begin{array}{c} \overline{y} \\ \frac{x \cdot y}{N}\end{array} \right ] [/tex]
Anybody have any hits/idear for to solve this assignment ??
Many thanks in advance
Sincerley Fred