Citation
Patent, Paul David (1972) Least Square Polynomial Spline Approximations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/G4VR-YF05. https://resolver.caltech.edu/CaltechTHESIS:06132016-132208506
Abstract
Bounds are derived for both the L2- and L∞-norms of the error in approximating sufficiently smooth functions by polynomial splines using an integral least square technique based on the theory of orthogonal projection in real Hilbert space. Quadrature schemes for the approximate solution of this least square problem are examined and bounds for the error due to the use of such schemes are derived. The question of the consistency of such quadrature schemes with the least square error is investigated and asymptotic results are presented. Numerical results are also included.
| Item Type: | Thesis (Dissertation (Ph.D.)) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subject Keywords: | (Mathematics) | ||||||||
| Degree Grantor: | California Institute of Technology | ||||||||
| Division: | Physics, Mathematics and Astronomy | ||||||||
| Major Option: | Mathematics | ||||||||
| Thesis Availability: | Public (worldwide access) | ||||||||
| Research Advisor(s): |
| ||||||||
| Thesis Committee: |
| ||||||||
| Defense Date: | 16 May 1972 | ||||||||
| Funders: |
| ||||||||
| Record Number: | CaltechTHESIS:06132016-132208506 | ||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:06132016-132208506 | ||||||||
| DOI: | 10.7907/G4VR-YF05 | ||||||||
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 9872 | ||||||||
| Collection: | CaltechTHESIS | ||||||||
| Deposited By: | INVALID USER | ||||||||
| Deposited On: | 13 Jun 2016 21:06 | ||||||||
| Last Modified: | 02 Jul 2024 19:44 |
Thesis Files
|
PDF
- Final Version
See Usage Policy. 18MB |
Repository Staff Only: item control page
