Diagonal elements of Cholesky factor. Each X ES+ has a unique Cholesky factorization X = LLT, where L is lower triangular, with Lii > 0. Show that Lii is a concave function of X (with domain S2+). Hint. Lii can be expressed as Lii = (wzTY-¹2) ¹/2, where is the leading i x i submatrix of X. Y [:]
Diagonal elements of Cholesky factor. Each X ES+ has a unique Cholesky factorization X = LLT, where L is lower triangular, with Lii > 0. Show that Lii is a concave function of X (with domain S2+). Hint. Lii can be expressed as Lii = (wzTY-¹2) ¹/2, where is the leading i x i submatrix of X. Y [:]
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
Quick plz...hand written..i'll give you multiple upvote
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbcc5df6-5e3f-42c6-b401-cfcf5239cffa%2F002b666c-9a44-49c0-8069-a01ba0162505%2Fugehzj7_processed.jpeg&w=3840&q=75)
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
![](/static/compass_v2/shared-icons/check-mark.png)
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
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)