Cholesky Factorization of the Generalized Symmetric k- Fibonacci Matrix
نویسندگان
چکیده
Matrix methods are a useful tool while dealing with many problems stemming from linear recurrence relations. In this paper, we discuss factorizations and inverse of two kinds generalized k-Fibonacci matrices. We derive some identities the sequence. investigate Cholesky factorization symmetric matrix by using these identities.
منابع مشابه
Perturbation analysis for the generalized Cholesky factorization
Let K be a symmetric indefinite matrix. Suppose that K 1⁄4 LJL is the generalized Cholesky factorization of K. In this paper we present perturbation analysis for the generalized Cholesky factorization. We obtain the first-order bound on the norm of the perturbation in the generalized Cholesky factor. Also, we give rigorous perturbation bounds. 2002 Elsevier Inc. All rights reserved.
متن کاملRigorous Multiplicative Perturbation Bounds for the Generalized Cholesky Factorization and the Cholesky–like Factorization
The generalized Cholesky factorization and the Cholesky-like factorization are two generalizations of the classic Cholesky factorization. In this paper, the rigorous multiplicative perturbation bounds for the two factorizations are derived using the matrix equation and the refined matrix equation approaches. The corresponding first-order multiplicative perturbation bounds, as special cases, are...
متن کاملThe generalized order-k Fibonacci–Pell sequence by matrix methods
In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, thenwe define a new recurrence, which we call generalized order-k F–P sequence. Also we present a systematic investigation of the generalized order-k F–P sequence. We give the generalized Binet formula, some identities and an explicit formula for sums of the generalized order-k F–P sequence by matrix me...
متن کاملOn the Stability of Cholesky Factorization for Symmetric Quasidefinite Systems
Sparse linear equations Kd r are considered, where K is a specially structured symmetric indefinite matrix that arises in numerical optimization and elsewhere. Under certain conditions, K is quasidefinite. The Cholesky factorization PKP T LDL T is then known to exist for any permutation P, even though D is indefinite. Quasidefinite matrices have been used successfully by Vanderbei within barrie...
متن کاملGeneralized (k, r)–Fibonacci Numbers
In this paper, and from the definition of a distance between numbers by a recurrence relation, new kinds of k–Fibonacci numbers are obtained. But these sequences differ among themselves not only by the value of the natural number k but also according to the value of a new parameter r involved in the definition of this distance. Finally, various properties of these numbers are studied.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Gazi university journal of science
سال: 2022
ISSN: ['2147-1762']
DOI: https://doi.org/10.35378/gujs.838411