Farooq, M and Salhi, A (2012) 'New recurrence relationships between orthogonal polynomials which lead to new Lanczostype algorithms.' Journal of Prime Research in Mathematics, 8. 61  75. ISSN 18173462

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Abstract
Lanczos methods for solving Ax = b consist in constructing a sequence of vectors (X ),k = 1,... such that r = bAX = P (A)r , where P is the orthogonal polynomial of degree at most k with respect to the linear functional c defined as c(ε ) = (y, A r ). Let P be the regular monic polynomial of degree k belonging to the family of formal orthogonal polynomials (FOP) with respect to c defined as c (ε ) = c(ε ). All Lanczostype algorithms are characterized by the choice of one or two recurrence relationships, one for P and one for P . We shall study some new recurrence relations involving these two polynomials and their possible combinations to obtain new Lanczostype algorithms. We will show that some recurrence relations exist, but cannot be used to derive Lanczostype algorithms, while others do not exist at all. k k k k 0 k 0 k k k i i (1) (1) (1) i i+1 (1)
Item Type:  Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science and Health > Mathematical Sciences, Department of 
Depositing User:  Jim Jamieson 
Date Deposited:  06 Aug 2013 10:58 
Last Modified:  07 Apr 2021 10:15 
URI:  http://repository.essex.ac.uk/id/eprint/7257 
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