Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Householder orthogonalization with a non-standard inner product (2104.04180v2)

Published 9 Apr 2021 in math.NA and cs.NA

Abstract: Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning of the input. However, in the context of a non-standard inner product, it becomes difficult to apply Householder orthogonalization due to the lack of an initial orthonormal basis. We propose strategies to overcome this obstacle and discuss algorithms and variants of Householder orthogonalization with a non-standard inner product. Theoretical analysis and numerical experiments demonstrate that our approach is numerically stable under mild assumptions.

Citations (2)

Summary

We haven't generated a summary for this paper yet.