Application Of The Gauss Newton Method

Submission: The report from part 4 including all relevant graphs and numerical analysis along with interpretations.

1) Which type of function (linear, exponential, or cubic) do you believe will best fit the data? Support your choice.

(–2, 4) and (1, 2) respectively in a two-dimensional plane using the printf() (only one is

Now the x - coordinate value of the vertex this time I can use to find the y – coordinate of the vertex.

to find solutions to the errors that were found so that a reoccurrence of the same error doesn’t

The alpha (α) is considered as the fittest solution. Beta (β) and delta (δ) are the second and third best solution, but the rest of the candidate solutions are assumed to be omega (ω).

The line is not a good fit because it does not match up with points exactly. I found the amplitude by finding the average height of each high, medium, and low point of the tides, and then taking the medium tide average and subtracting that from the high tide average. Then, I took the low tide average and subtracted that from the medium tide average. From subtracting the medium from the high tide averages I got .748, and from subtracting the low from the medium tide averages I got .741. Next, I took these two numbers, added them and then divided that by two which gave me my amplitude of .7445. To find the period I took the middle point of the high points and the middle point of the low points and subtracted the time value of each of those, which gave me six. Then I put two pie over six which reduces to pie over three and in decimal form equals 1.04. My phase shit was five because my first x-value was five given from the tide website. My vertical shift was .997 and I found that by taking all of the middle points and taking the average of those. I used cosine instead of sine because my graph started at the amplitude and went towards the middle instead of going from the middle to the

The suitability of the polynomial model equation was judged by determining R2 and its significance was determined by using

where dPmax is the maximum change in pressure, k is angular wave number, and w is angular frequency.

The line of best-fit is used to find the gradient, the T2/L value, if straight or linear it shows that the relationship between the two is directly proportional. Using the original equation, you can square both sides and rearrange it to make . Then you can input the gradient value (T2/L) and work out g. , where g equals 10.13 m/s2. This value is close to the

Using TI InterActive!™ to graph that function, overlaid with the original data, and restricting the graph of the function to the same domain and range as the domain and range on the scatterplot, the graph is as follows:

The thermal models are governed by following equations. Where Rhs is the total thermal resistance of a heatsink, which is summation of thermal resistance of the fin (Rf) and thermal resistance of the base (Rb).

Figure 3 is a diagram indicating the application of this method to a hyperbolic paraboloid.

For the regularization problem: minβ+ 2σL2 + 2σ12 , let R, E the value of the residual and

5. Represent each block in the form of a training vector space X. Each block is converted to the training vector Xi= (xi1, xi2, xik).