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Consider the matrix of Hibert H100 and the system HX = b, where b is a...

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Advance Math

Consider the matrix of Hibert H100 and thesystem HX = b, where b is a columnvector from 1 to 100. Solve the system in the following three ways-->

1) X = H-1 b

2) Using the factorization H = LU

3) Using the factorization H = QR

Premultiplica H for each of the three solution vectorsand make the comparison with vector b.

What method gives a better solution?

Answer & Explanation Solved by verified expert
4.0 Ratings (579 Votes)
function comparluqr Hhilb100 b11100 bb Direct inverse method x1invHb LU decomposition LUluH yL x2Uy QR decomposition QRqrH yQ x3Ry b1Hx1 b2Hx2 b3Hx3 solutionb1b2b3 end Output solution 10e03 52502 00010 00010 50870 00020 00020 49308 00030 00030 47819 00040 00040 46406 00050 00050 45067 00060 00060 43800 00070 00070 42600 00080 00080 41463 00090 00090 40385 00100 00100 39362 00110 00110 38391 00120 00120 37467    See Answer
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