# Iterative methods

1. Jul 26, 2006

### eljose

let be the integral equation:

$$f(x)=\lambda \int_{0}^{1}dyK(x,y)f(y)$$

where the Kernel is known and "lambada" is an small eigenvalue... the question is if i want to solve i propose the iterative scheme:

$$f_{n+1} (x)=\lambda \int_{0}^{1}dyK(x,y)f_n(y)$$

My question is if in this case i can propose a "Neumann series" for the resolvent Kernel R(x,y) in the form...

$$R= \sum_{n=0}^{\infty} \lambda ^ n K^{n}$$

for K^n the n-th iterated kernel since the equation is HOmogeneus (all the functions involved except the Kernel are unknown) or if we have enough with the iteration procedure to solve the equation..thanks.

2. Jul 26, 2006

### HallsofIvy

Staff Emeritus
"lambda" is an eigenvalue. "Lambada" is a dance!

3. Aug 9, 2006

### pezze

:rofl: :rofl: :rofl:

4. Aug 25, 2006

### lokofer

- Ooooh...¡what a wonderful and marvelous joke¡¡..I ask myself daily why you are here wasting your time when you could be a "millionaire" Hollywood comediant like Eddie Murphy or appear on "Saturday Night LIfe"....

5. Aug 26, 2006

### HallsofIvy

Staff Emeritus