Polynomial - Newton's Method (2 Viewers)

[study-freak]

Using Newton's Method, under what conditions will a better estimate NOT be reached?

If the initial estimate is at a stationary point or if there is a turning point between the initial estimate and the actual root...

Or if at P(z₁) and P''(z₁) have opposite signs, where x=z₁ is the first approximation.

I never really encountered a question that involved the closeness of a root. I shall have a look later but nevertheless the signs of P(z₁) and P"(z₁) do matter, which is what I said initially.

Now, you've initially stated that if "P(z₁) and P''(z₁) have opposite signs, where x=z₁ is the first approximation," a better estimate NOT be reached using Newton's Method.
That's a bit more than "the signs of P(z₁) and P"(z₁) do matter."

 

[cutemouse]

Now, you've initially stated that if "P(z₁) and P''(z₁) have opposite signs, where x=z₁ is the first approximation," a better estimate NOT be reached using Newton's Method.
That's a bit more than "the signs of P(z₁) and P"(z₁) do matter."

Yes the signs of P(z₁) and P''(z₁) must be the same for a good 1st approximation using Newton's method of estimating roots to polynomials.

 

[study-freak]

Now, you've initially stated that if "P(z₁) and P''(z₁) have opposite signs, where x=z₁ is the first approximation," a better estimate NOT be reached using Newton's Method.
That's a bit more than "the signs of P(z₁) and P"(z₁) do matter."

Yes the signs of P(z₁) and P''(z₁) must be the same for a good 1st approximation using Newton's method of estimating roots to polynomials.

Again, there is a difference between 'if "P(z₁) and P''(z₁) have opposite signs, where x=z₁ is the first approximation," a better estimate NOT be reached using Newton's Method' and "the signs of P(z₁) and P''(z₁) must be the same for a good 1st approximation using Newton's method of estimating roots to polynomials."

 

[cutemouse]

I'll take silence as a concession of defeat.

Lol.

Sometimes you gotta pick which battles to fight and ask yourself the question "If I win this battle, what do I gain from it?". There's no point in winning some stupid battle if I'm going to waste all my time and energy and get no reward or prize.

Maybe that's some wisdom for ya

I actually was going to reply as soon as I got hold of my Coroneos books again, but I guess it's easier not doing so .