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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Urgent plzz..hand written

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.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

