Exercise · ZW-CHOLESKY-FACTORIZATION-005 · ★★☆ Intermediate
What is the relation between Cholesky and LU for a symmetric positive definite matrix?
Choose one option.
Show answer
- B. Cholesky requires about half as many operations as LU
Explanation
Exploiting symmetry reduces Cholesky's cost to roughly half that of LU. The other options deny that advantage or state something false about LU.
Review the concept: Cholesky factorization
The Cholesky factorization decomposes a symmetric positive definite matrix \(A\) as \(A = LL^{T}\), where \(L\) is lower triangular with positive diagonal.
\[A = LL^{T}, \; l_{jj} = \sqrt{a_{jj} - \sum_{k
More practice problems: cholesky factorization
- ZW-CHOLESKY-FACTORIZATION-001 What property must a matrix A have to apply the Cholesky factorization?
- ZW-CHOLESKY-FACTORIZATION-002 What form does the factor L have in A = LL^T?
- ZW-CHOLESKY-FACTORIZATION-003 If L is the Cholesky factor, what does the equality A = LL^T express?
- ZW-CHOLESKY-FACTORIZATION-004 What is the element l_11 of the Cholesky factor when a_11=9?
- ZW-CHOLESKY-FACTORIZATION-006 Compute l_11 and l_21 for A=[4 2; 2 5].
- ZW-CHOLESKY-FACTORIZATION-007 If a_22=10 and l_21=3, what is l_22?
- ZW-CHOLESKY-FACTORIZATION-008 For A=[9 3; 3 5], what is the factor L?
- ZW-CHOLESKY-FACTORIZATION-009 If L=[2 0; 1 2], what is the product LL^T?
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