{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Slides_2010_02_12

# Slides_2010_02_12 - Applied linear algebra and numerical...

This preview shows pages 1–6. Sign up to view the full content.

Applied linear algebra and numerical analysis Session 17 Prof. Ulrich Hetmaniuk Department of Applied Mathematics February 12, 2010

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Who are they?
Gram-Schmidt process In a real linear space equipped with an inner product, the Gram-Schmidt process will convert any arbitrary basis into an orthogonal basis.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Gram-Schmidt process Consider the vectors a 1 = 1 1 - 1 a 2 = 1 0 2 a 3 = 2 - 2 3 Compute q 1 such that a 1 = α q 1 k q 1 k 2 = 1. Compute q 2 such that a 2 = β q 1 + γ q 2 q T 1 q 2 = 0 and k q 2 k 2 = 1. Compute q 3 such that a 3 = δ q 1 + ε q 2 + ζ q 3 q T 1 q 3 = 0, q T 2 q 3 = 0, and k q 3 k 2 = 1. q 1 = 1 3 1 1 - 1 q 2 = 1 42 4 1 5 q 3 = 1 14 2 - 3 - 1
Gram-Schmidt process Consider the basis vectors a 1 , a 2 , a 3 . We want to build the sequence of orthonormal vectors q 1 , q 2 , q 3 such that span ( a 1 ,..., a j ) = span ( q 1 ,..., q j ) j = 1 ,..., 3 . (1) a 1 = r 11 q 1 a 2 = r 12 q 1 + r 22 q 2 q T 1 a 2 = r 12 q T 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 22

Slides_2010_02_12 - Applied linear algebra and numerical...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online