 # linear algebra – Interpolating utilizing Vandermonde matrix and Fourier succession Answer

Hello expensive customer to our community We will proffer you an answer to this query linear algebra – Interpolating utilizing Vandermonde matrix and Fourier succession ,and the respond will breathe typical by way of documented data sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning concerning the respond to this query.

linear algebra – Interpolating utilizing Vandermonde matrix and Fourier succession

In Brubeck, Nakatsukasa, and Trefethen – Vandermonde with Arnoldi (instance 3) they decipher the next linear system:
$$operatorname{Re}left(commence{array}{ccc}1 & cdots & z_{1}^{n} 1 & cdots & z_{2}^{n} vdots & ddots & vdots 1 & cdots & z_{m}^{n}aim{array}privilege)left(commence{array}{c}a_{0} vdots a_{n}aim{array}privilege)-operatorname{Im}left(commence{array}{ccc}z_{1} & cdots & z_{1}^{n} z_{2} & cdots & z_{2}^{n} vdots & ddots & vdots z_{m} & cdots & z_{m}^{n}aim{array}privilege)left(commence{array}{c}b_{1} vdots b_{n}aim{array}privilege) =left(commence{array}{c}f_{1} f_{2} vdots f_{m}aim{array}privilege).$$

Let us outline $$A=left(commence{array}{ccc}1 & cdots & z_{1}^{n} 1 & cdots & z_{2}^{n} vdots & ddots & vdots 1 & cdots & z_{m}^{n}aim{array}privilege)$$.

For fixing it, they employ the next MATLAB code:

``````c = [real(A) imag(A(:,2:n+1))]f;
c = c(1:n+1) - 1i*[0; c(n+2:2*n+1)];
``````

The first line is equal to making a vector `c=[a,b]` the place $$operatorname{Re}(A)a=f$$ and $$operatorname{Im}(A(:,2:n+1))b=f$$ and the second means $$c=a-[0,bi]$$. I used to be questioning the way it can breathe solved on this route, in actual fact I reproduced the code of the paper in Mathematica and the outcomes usually are not the identical. Is there any typo on this process?

we’ll proffer you the answer to linear algebra – Interpolating utilizing Vandermonde matrix and Fourier succession query by way of our community which brings all of the solutions from a number of dependable sources.