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Diagonal elements of Cholesky factor. Each X ES+ has a unique Cholesky factorization X = LLT, where L is lower triangular, with Li> 0. Show that Lii is a concave function of X (with domain S2+). Hint. Lii can be expressed as Lii = (w - zTY-12) ¹/2, where is the leading ix i submatrix of X. Y T 2 W

Diagonal elements of Cholesky factor. Each X ES+ has a unique Cholesky factorization X = LLT, where L is lower triangular, with Li> 0. Show that Lii is a concave function of X (with domain S2+). Hint. Lii can be expressed as Lii = (w - zTY-12) ¹/2, where is the leading ix i submatrix of X. Y T 2 W

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3.27 Diagonal elements of Cholesky factor. Each X E S has a unique Cholesky factorization X = LLT, where L is lower triangular, with Lü > 0. Show that Lii is a concave function of X (with domain S). Hint. Lii can be expressed as Lii = (w – zTY-12)/2, where Y T w is the leading i xi submatrix of X.
Transcribed Image Text:3.27 Diagonal elements of Cholesky factor. Each X E S has a unique Cholesky factorization X = LLT, where L is lower triangular, with Lü > 0. Show that Lii is a concave function of X (with domain S). Hint. Lii can be expressed as Lii = (w – zTY-12)/2, where Y T w is the leading i xi submatrix of X.
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