Media Summary: RungeBot on both twitter (for now!) and mastodon. Yes, I'm on ... The Wolfram Demonstrations Project contains thousands of free ... Polynomial wiggle observed at the edges of Interval.

Beware The Runge Spikes - Detailed Analysis & Overview

RungeBot on both twitter (for now!) and mastodon. Yes, I'm on ... The Wolfram Demonstrations Project contains thousands of free ... Polynomial wiggle observed at the edges of Interval. High degree polynomials should get better as they fit more points. Yet something strange happens near the edges. This visual ... At first glance, the remainder formula for Lagrange polynomials seems to say that more points are better. In a lot of situations this ... The Remez algorithm on a equispaced reference set.

A tour of interpolation, starting with a simple example and ending with completely unexpected and beautiful convergence results.

Photo Gallery

Beware the Runge Spikes!
Runge's Phenomenon
polynomial wiggle and Runge's phenomenon
Runge's Phenomenon: Equidistant vs Chebyshev Nodes
Runge's Phenomenon
Runge's Phenomenon
Runge function
The Runge Function, Polynomial Interpolation, and the Cauchy Residual Theorem
Runge’s Approximation Theorem
Runge's Phenomenon M3.11 - Intro to DG
View Detailed Profile
Beware the Runge Spikes!

Beware the Runge Spikes!

RungeBot on both twitter (for now!) and mastodon. https://twitter.com/rungebot https://mathstodon.xyz/@RungeBot Yes, I'm on ...

Runge's Phenomenon

Runge's Phenomenon

http://demonstrations.wolfram.com/RungesPhenomenon The Wolfram Demonstrations Project contains thousands of free ...

polynomial wiggle and Runge's phenomenon

polynomial wiggle and Runge's phenomenon

Polynomial wiggle observed at the edges of Interval.

Runge's Phenomenon: Equidistant vs Chebyshev Nodes

Runge's Phenomenon: Equidistant vs Chebyshev Nodes

High degree polynomials should get better as they fit more points. Yet something strange happens near the edges. This visual ...

Runge's Phenomenon

Runge's Phenomenon

At first glance, the remainder formula for Lagrange polynomials seems to say that more points are better. In a lot of situations this ...

Runge's Phenomenon

Runge's Phenomenon

http://demonstrations.wolfram.com/RungesPhenomenon/ The Wolfram Demonstrations Project contains thousands of free ...

Runge function

Runge function

The Remez algorithm on a equispaced reference set.

The Runge Function, Polynomial Interpolation, and the Cauchy Residual Theorem

The Runge Function, Polynomial Interpolation, and the Cauchy Residual Theorem

A tour of interpolation, starting with a simple example and ending with completely unexpected and beautiful convergence results.

Runge’s Approximation Theorem

Runge’s Approximation Theorem

Runge’s Approximation Theorem

Runge's Phenomenon M3.11 - Intro to DG

Runge's Phenomenon M3.11 - Intro to DG

Runge's Phenomenon M3.11 - Intro to DG