Numerical strategies to reduce the effect of ill-conditioned correlation matrices and underflow errors in kriging (Record no. 21103)
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| fixed length control field | a |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240530100714.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240530b xxu||||| |||| 00| 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | AIKTC-KRRC |
| Transcribing agency | AIKTC-KRRC |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| 9 (RLIN) | 23530 |
| Author | Haarhoff, Lukas J. |
| 245 ## - TITLE STATEMENT | |
| Title | Numerical strategies to reduce the effect of ill-conditioned correlation matrices and underflow errors in kriging |
| 250 ## - EDITION STATEMENT | |
| Volume, Issue number | Vol.135(4), Apr |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. | |
| Place of publication, distribution, etc. | New York |
| Name of publisher, distributor, etc. | ASME |
| Year | 2013 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Pagination | 1-4p. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Kriging is used extensively as a metamodel in multidisciplinary design optimization. The correlation matrix used in Kriging metamodeling frequently becomes ill-conditioned. Therefore different numerical methods used to solve the Kriging equations affect the search for the optimum Kriging parameters and the ability of the Kriging surface to accurately interpolate known data points. We illustrate this by firstly computing the inverse of the correlation matrix in the Kriging equations, and secondly by solving the systems of equations using decomposition and back substitution, thereby avoiding the inversion of the correlation matrix. Our results clearly show that by decomposing and back substituting, the interpolation accuracy is maintained for significantly higher condition numbers. We then show that computing the natural logarithm of the determinant using additive calculations as opposed to multiplicative calculations significantly reduces numerical underflow errors encountered when searching for the optimum Kriging parameters. Although the effect of decomposition and back substitution are known, and the underflow difficulties when computing the natural logarithm of the determinant of the correlation matrix has been mentioned in passing in Kriging literature, this work clearly quantifies and reinforces these methods, hopefully for the benefit of researchers entering the field. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| 9 (RLIN) | 4626 |
| Topical term or geographic name entry element | Mechanical Engineering |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| 9 (RLIN) | 23531 |
| Co-Author | Kok, Schalk |
| 773 0# - HOST ITEM ENTRY | |
| Title | Journal of mechanical design |
| Place, publisher, and date of publication | New York ASME |
| 856 ## - ELECTRONIC LOCATION AND ACCESS | |
| URL | https://asmedigitalcollection.asme.org/mechanicaldesign/article-abstract/135/4/044502/375664/Numerical-Strategies-to-Reduce-the-Effect-of-Ill?redirectedFrom=fulltext |
| Link text | Click here |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Dewey Decimal Classification |
| Koha item type | Articles Abstract Database |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Home library | Current library | Shelving location | Date acquired | Total Checkouts | Barcode | Date last seen | Price effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | School of Engineering & Technology | School of Engineering & Technology | Archieval Section | 30/05/2024 | 2024-0671 | 30/05/2024 | 30/05/2024 | Articles Abstract Database |