Fifth Assignment of Financial Computation

Fifth assignment of Financial Computation

1.Suppose that the interpolation polynomial is in the form,hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the hen﷽﷽﷽﷽﷽﷽﷽) increasingnts, the

The more polynomials it involve , the more precise it would be. Chebyshev nodes are the roots of the Chebyshev polynomial of the first kind. They are often used as nodes in polynomial interpolation because the resulting interpolation polynomial minimizes the Runge's phenomenon.

2. A Hilbert matrix, is a square matrix with entries being the unit fractions

Codes：

N=10;

for i=1:N;

for j=1:N,

A(i,j)=1/(i+j-1);

end

end

Result：

>> A

A =

1.0000 0.5000 0.3333 0.2500 0.2000 0.1667 0.1429 0.1250 0.1111 0.1000

0.5000 0.3333 0.2500 0.2000 0.1667 0.1429 0.1250 0.1111 0.1000 0.0909

0.3333 0.2500 0.2000 0.1667 0.1429 0.1250 0.1111 0.1000 0.0909 0.0833

0.2500 0.2000 0.1667 0.1429 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769

0.2000 0.1667 0.1429 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714

0.1667 0.1429 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.0667

0.1429 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625

0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.0588

0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.0588 0.0556

0.1000 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.0588 0.0556 0.0526

>> cond(A)

ans =

1.6025e+13

The matrix is very nearly singular. In such...