Page 72 - Applied Numerical Methods Using MATLAB

PROBLEMS 61
means the solution for which the residual error (||Ax − b||)isthe
minimum over the many solutions.
1.15 Operations on Vectors
(a) Find the mathematical expression for the computation to be done by
the following MATLAB statements.

>>n = 0:100; S = sum(2.^-n)
(b) Write a MATLAB statement that performs the following computation.

10000 2

1 π
−
(2n + 1) 2 8
n=0
(c) Write a MATLAB statement which uses the commands prod() and
sum() to compute the product of the sums of each row of a 3 × 3
random matrix.
(d) How does the following MATLAB routine “repetition(x,M,m)” con-
vert a given row vector sequence x to make a new sequence y ?

function y = repetition(x,M,m)
ifm==1
MNx = ones(M,1)*x; y = MNx(:)’;
else
Nx = length(x); N = ceil(Nx/m);
x = [x zeros(1,N*m - Nx)];
MNx = ones(M,1)*x;
y = [];
for n = 1:N
tmp = MNx(:,(n - 1)*m + [1:m]).’;
y = [y tmp(:).’];
end
end

(e) Make a MATLAB routine “zero_insertion(x,M,m)”, which inserts
m zeros just after every Mth element of a given row vector sequence
x to make a new sequence. Write a MATLAB statement to apply the
routine for inserting two zeros just after every third element of x =
[ 1372 49 ]toget

y = [ 1370 024 900 ]

(f) How does the following MATLAB routine “zeroing(x,M,m)” convert
a given row vector sequence x to make a new sequence y?