- 1.
- (10 minutes) Given is a residual where
The data is .The fitting functions are the column vectors
, , and ,and the model parameters are the scalars
*m*,_{1}*m*, and_{2}*m*. Suppose that_{3}*m*and_{1}*m*are already known. Derive a formula for finding_{2}*m*that minimizes the residual length (squared) ._{3} - 2.
- (10 minutes)
Below is a subroutine written in a mysterious dialect of Fortran.
Describe ALL the inputs required
for this subroutine to multiply a vector times
the
*transpose*of a matrix.# matrix multiply and its adjoint # subroutine matmult( adj, bb, x,nx, y,ny) integer ix, iy, adj, nx, ny real bb(ny,nx), x(nx), y(ny) if( adj == 0 ) do iy= 1, ny y(iy) = 0. else do ix= 1, nx x(ix) = 0. do ix= 1, nx { do iy= 1, ny { if( adj == 0 ) y(iy) = y(iy) + bb(iy,ix) * x(ix) else x(ix) = x(ix) + bb(iy,ix) * y(iy) }} return; end

4/27/2004