Solution Of Block-Structured Least-Squares Problems

Charles R. Crawford

doi:10.1117/12.959074

16 September 1980 Solution Of Block-Structured Least-Squares Problems

Charles R. Crawford

Proceedings Volume 0237, 1980 International Lens Design Conference; (1980) https://doi.org/10.1117/12.959074
Event: 1980 International Lens Design Conference, 1980, Oakland, United States

Abstract

The design of multi-configuration optical systems leads to the minimization of a merit function whose terms are most conveniently evaluated in groups. The Jacobian or difference matrix associated with these merit functions can be decomposed into blocks corresponding to these groups. The associated constrained least-squares problem can be solved without requiring that more than two or three blocks be in high-speed memory at one time. The algorithm described here is useful for lens-design programs running on mini-computers where high-speed memory is limited but medium-speed storage such as disc is available. An orthogonal factorization of the matrix is obtained so that rank-deficient problems can be handled in a consistent and numerically stable manner. This factorization can be used as an adjunct to a variety of least-squares type algorithms.

Citation Download Citation

Charles R. Crawford "Solution Of Block-Structured Least-Squares Problems", Proc. SPIE 0237, 1980 International Lens Design Conference, (16 September 1980); https://doi.org/10.1117/12.959074

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available