Fiveable
Fiveable

or

Log in

Find what you need to study


Light

Find what you need to study

10.12 Lagrange Error Bound

1 min readjune 7, 2020

Athena_Codes

Athena_Codes

Athena_Codes

Athena_Codes

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(565).png?alt=media&token=e73e405a-abce-40b3-8d0b-6b825d0534c6

Sometimes, we want to find out how accurate a prediction is to the actual function value at a given x. This is where the comes into play.

What is the Lagrange Error Bound and how do we find it?

When we have the below, notice how similar it is to the from earlier!

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(795).png?alt=media&token=69b77a84-5a32-4573-8046-1b28ce13614a

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(796).png?alt=media&token=29108ee8-31dc-4530-9ae9-f7cdc0c2c93c

Problems

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(798).png?alt=media&token=654132da-3f21-4b1a-a637-852cda54a0d3

Key Terms to Review (3)

Alternating Series Error Bound

: The alternating series error bound provides an upper bound on the absolute error when approximating an alternating series using only a finite number of terms. It helps determine how close our partial sum is to the actual value of the series.

Lagrange Error Bound

: The Lagrange error bound gives an upper bound on the absolute error between an actual value and its approximation using a Taylor polynomial. It helps determine how close our estimation is to the true value.

Taylor Polynomial

: A Taylor polynomial is a polynomial approximation of a function centered around a specific point. It is used to estimate the value of the function at nearby points.

10.12 Lagrange Error Bound

1 min readjune 7, 2020

Athena_Codes

Athena_Codes

Athena_Codes

Athena_Codes

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(565).png?alt=media&token=e73e405a-abce-40b3-8d0b-6b825d0534c6

Sometimes, we want to find out how accurate a prediction is to the actual function value at a given x. This is where the comes into play.

What is the Lagrange Error Bound and how do we find it?

When we have the below, notice how similar it is to the from earlier!

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(795).png?alt=media&token=69b77a84-5a32-4573-8046-1b28ce13614a

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(796).png?alt=media&token=29108ee8-31dc-4530-9ae9-f7cdc0c2c93c

Problems

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(798).png?alt=media&token=654132da-3f21-4b1a-a637-852cda54a0d3

Key Terms to Review (3)

Alternating Series Error Bound

: The alternating series error bound provides an upper bound on the absolute error when approximating an alternating series using only a finite number of terms. It helps determine how close our partial sum is to the actual value of the series.

Lagrange Error Bound

: The Lagrange error bound gives an upper bound on the absolute error between an actual value and its approximation using a Taylor polynomial. It helps determine how close our estimation is to the true value.

Taylor Polynomial

: A Taylor polynomial is a polynomial approximation of a function centered around a specific point. It is used to estimate the value of the function at nearby points.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.