Question
Download Solution PDFCholesky decomposition is carried out on the following square matrix [๐ด].
\(\rm [A]=\begin{bmatrix}8&-5\\\ -5&a_{22}\end{bmatrix}\)
Let ๐ij and ๐ij be the (i, j)th elements of matrices [๐ฟ] and [๐ด], respectively. If the element ๐22 of the decomposed lower triangular matrix [๐ฟ] is 1.968, what is the value (rounded off to the nearest integer) of the element ๐22?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLLT = A
\(\begin{bmatrix}L_{11}&0\\\ L_{21}&L_{22} \end{bmatrix} \begin{bmatrix} L_{11}&L_{21}\\\ 0&L_{22} \end{bmatrix}= \begin{bmatrix} 8&-5\\\ -5&a_{22} \end{bmatrix}\)
L11 = 2√2 , L21 = \(-\frac{5}{2\sqrt2}\) and \(L^2_{21}+L^2_{22}=a_{22}\)
\(a_{22}=\left( -\frac{5}{2\sqrt2} \right)^2\) + 1.968 = 6.99 โ 7
Last updated on Jan 8, 2025
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