Thanks a lot for sharing these courses, Just one comment, at 2:30 we have Vandermonde matrix. the matrix is highly ill-conditioned for large N. We may use a Lagrange base instead with careful choice of x to avoid the Runge phenomena.
You are absolutely right! In this course we deal only with very small matrices and I design the homework so students will not run into problems. I consider Lagrange interpolation and associated topics outside the scope of this course which is very applied, but you have motivated me to add a note in the lecture about this for interested students. Thank you! Keep the comments and suggestions coming!
Thank you for the simple explanation.
Thanks a lot for sharing these courses, Just one comment, at 2:30 we have Vandermonde matrix. the matrix is highly ill-conditioned for large N. We may use a Lagrange base instead with careful choice of x to avoid the Runge phenomena.
You are absolutely right! In this course we deal only with very small matrices and I design the homework so students will not run into problems. I consider Lagrange interpolation and associated topics outside the scope of this course which is very applied, but you have motivated me to add a note in the lecture about this for interested students.
Thank you! Keep the comments and suggestions coming!
How large shoild be the max value of the.matrix in your opinion?
I mean what value of N be?