- #1
John3509
- 53
- 3
So I was trying to understand Horner's method. I understand that you can take a polynomial and factor out the x's and re write it as multiple linear functions recursively plugged into each other and that this makes evaluating a polynomial easier because you just evaluate a linear function multiple times. But
I was reading the Wikipedia page and I do not understand:
-What does this have to do with synthetic division? I know what synthetic division is, I just don't see the conection.
-What does this that to do with Newtons method for calculating the root of a function? I know that Newtons method also involves recursive evaluation where the previous result is the new input. Newtons method comes from the linearization, but besides that similarity, I also do not see the connection here.
-After the words Now, it can be proven that; under the Description of the algorithm section, I do not understand where it gets that equation from? If b_0 is p(x_0) then if you rearrange the terms you have slope equals that polynomial of b's , which I don't understand why they would set that equal to the slope?
-And why replace the coefficient a with b ?
Also I was watching this video on Horner's method. At 2:47 , the last bullet point, the representation as a piece wise defined function I do not understand.
And finally, I don't get why I don't get this, its all just elementary operations!
I was reading the Wikipedia page and I do not understand:
-What does this have to do with synthetic division? I know what synthetic division is, I just don't see the conection.
-What does this that to do with Newtons method for calculating the root of a function? I know that Newtons method also involves recursive evaluation where the previous result is the new input. Newtons method comes from the linearization, but besides that similarity, I also do not see the connection here.
-After the words Now, it can be proven that; under the Description of the algorithm section, I do not understand where it gets that equation from? If b_0 is p(x_0) then if you rearrange the terms you have slope equals that polynomial of b's , which I don't understand why they would set that equal to the slope?
-And why replace the coefficient a with b ?
Also I was watching this video on Horner's method. At 2:47 , the last bullet point, the representation as a piece wise defined function I do not understand.
And finally, I don't get why I don't get this, its all just elementary operations!