aitken.rs

/// Accelerate convergence of a sequance, using Aitken acceleration
fn aitken(v: &Vec<f64>) -> Vec<f64>{
    let n = v.len();
    let mut v_ = vec![0.0; n-2];
    for i in 0..(n-2){
        v_[i] = v[i] - (v[i+1]-v[i])*(v[i+1]-v[i])/(v[i+2]-2.0*v[i+1]+v[i])
    }
    v_
}

/// Create a vector of \sum_{i=1}^{n} 1/i^2
fn invsqrsum(n: i32) -> Vec<f64>{
    let mut v = vec![0.0; n as usize];
    for idx in 0..n {
        let mut cum = 0.0;
        for i in 1..idx+2{
            // accumurate from small values to reduce errors
            cum += 1.0/(((idx+2-i)*(idx+2-i)) as f64)
        }
        v[idx as usize] = cum
    }
    v
}

fn print_seq(xs: &Vec<f64>){
    let n = xs.len();
    for i in 0..(n-1){
        print!("{:.6}, ", xs[i])
    }
    print!("{:.6}", xs[n-1])
}

fn main(){
    let mut v = invsqrsum(20);
    for i in 0..10{
        println!("xs^{}:", i);
        print_seq(&v);
        println!("");
        v = aitken(&v);
    }
}