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1.
(b)
The folowing the minimization function for Ruotient using cyclic coordinate descent:
```{r}
solveRayleigh2 <- function (A,B,eps = 1e-6, itmax = 100) {
x <- rep(1,4)
itel <- 1
repeat {
    tmax <- 0
    for (j in 1:4) {
      u <- A%*%x
      v <- B%*%x
      a.jj <- A[j,j]
      b.jj <- B[j,j]
      u.j <- u[j]
      v.j <- v[j]
      quad.a <- b.jj*u.j - a.jj*v.j
      quad.b <- t(x)%*%A%*%x*b.jj - t(x)%*%B%*%x*a.jj
      quad.c <- t(x)%*%A%*%x*v.j - t(x)%*%B%*%x*u.j
      
      theta <- min.quadratic.solution(quad.a,quad.b,quad.c)   
      x[j] <- x[j] + theta   
      tmax <- max (tmax, abs(theta))
    }
    if ((tmax < eps) || (itel == itmax)) break()
    itel <- itel + 1
}
list(min.x=x, min.lambda=t(x)%*%A%*%x/(t(x)%*%B%*%x))
}...

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