%Math 128B Spring 2005
%Hmwk1 - Solutions (Jan. 26, 2005)

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function	CosInterval()
%see Help: "Plot[2]"

%create vector of equally spaced x-values
x	= linspace(-1,1);
%create vector of function values (y-values)
y	= cos(x);
%display the graph
plot(x,y)

%improve appearance
axis([-1 1 0 1.01])	%provide some whitespace above graph
ylabel('cos(x)')
title('Math128 - Hmwk1.1')
text(-0.2,1/3,'{\it Graph of the cosine function}')

return

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%called with ssolve(10, 0.1, 30) and ssolve(4, -0.05, 50)
function	result = ssolve(a,b,n)

%enable plotting within function for Problem #3
doPlot	= 1;

%create the matrix M
M		= eye(n);
M(1,2)	= a;
M(n,1:n-1)	= b;

%create the row vector y
y		= 1:n;

%solve M*result = y'
result	= M\y';	%WHY NOT inv(M)*y' ?
				%see Help: "division matrix(arithmetic...)"

if doPlot
	plot([1:n],result);
	title('Math128 - Hmwk1.3')
end

return

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function	HInv	= HilbertInv(n)

%flag for enabling/disabling debug information
Debug	= 1;

%create the Hilbert matrix
H	= zeros(n);

for i=1:n
	for j=1:n	%j=i:n could be used to avoid redundant computation
		H(i,j) = 1/(i+j-1);
	end		%inner j-loop for columns
end		%outer i-loop for rows

%return the inverse Hilbert matrix
HInv	= inv(H);

if Debug
	%display this during debugging
	norm(H - hilb(n),inf)		%compare our H with Matlab's
	norm(HInv - invhilb(n),inf)	%compare our HInv with Matlab's
end

return