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Paper Abstract and Keywords
Presentation 2007-08-06 12:10
Accurate Cholesky Decomposition Method for Ill-conditioned Matrices -- Fast Detection of Positive Definiteness --
Shin'ichi Oishi (Waseda Univ.) NLP2007-42
Abstract (in Japanese) (See Japanese page) 
(in English) In this paper, we will present an accurate Cholesky decomposition algorithm.

For the purpose, we develope multiple precision algorithms for the four basic arithmetic operations
and the square root operation.
Let $A=[A_1,A_2,\cdots,A_K]$ and $B=[B_1,B_2,\cdots,B_L]$ are $K$-tuple and $L$-tuple numbers. Here, $A_i \in \F$ for
$i=1,2,\cdots,K$ and $B_i \in \F$ for $i=1,2,\cdots,L$. For simplicity, we assume that $K=max(K,L)$
Then, the following becomes multiple precision addition with $K$-fold accuracy:
Keyword (in Japanese) (See Japanese page) 
(in English) Ill-conditioned Matrices / Cholesky Decomposition / Positive Definiteness / / / / /  
Reference Info. IEICE Tech. Rep., vol. 107, no. 184, NLP2007-42, pp. 35-37, Aug. 2007.
Paper # NLP2007-42 
Date of Issue 2007-07-30 (NLP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF NLP2007-42

Conference Information
Committee NLP  
Conference Date 2007-08-06 - 2007-08-07 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To NLP 
Conference Code 2007-08-NLP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Accurate Cholesky Decomposition Method for Ill-conditioned Matrices 
Sub Title (in English) Fast Detection of Positive Definiteness 
Keyword(1) Ill-conditioned Matrices  
Keyword(2) Cholesky Decomposition  
Keyword(3) Positive Definiteness  
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1st Author's Name Shin'ichi Oishi  
1st Author's Affiliation Waseda University (Waseda Univ.)
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Speaker Author-1 
Date Time 2007-08-06 12:10:00 
Presentation Time 25 minutes 
Registration for NLP 
Paper # NLP2007-42 
Volume (vol) vol.107 
Number (no) no.184 
Page pp.35-37 
#Pages 3 
Date of Issue 2007-07-30 (NLP) 

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