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Inversion of Large, Symmetric, Positive Definite, Non Sparse Matrices

IP.com Disclosure Number: IPCOM000054654D
Original Publication Date: 1980-Mar-01
Included in the Prior Art Database: 2005-Feb-13

Publishing Venue

IBM

Related People

Authors:
Johnson, TA [+details]

Abstract

The inversion of large, non-sparse, symmetric, positive definite matrices using a fixed amount of primary storage, regardless of matrix size, is accomplished by means of (1) a custom-tailored paging scheme for retrieval of matrix elements and (2) the structuring of calculations to permit maximum usage of main storage resident data, thereby minimizing data fetches. The technique utilizes secondary storage devices (disk, drum, etc.) to hold the input matrix and its inverse. Only a small portion of the entire input or output matrix is required to be resident in main memory at any time. In this way, very large problems may be solved which cannot otherwise be tackled even by the largest virtual machines.