Cholesky Factorizations of Matrices Associated with r-Order Recurrent Sequences
نویسنده
چکیده
In this paper we extend some results on the factorization of matrices associated to Lucas, Pascal, Stirling sequences by the Fibonacci matrix. We provide explicit factorizations of any matrix by the matrix associated with an r-order recurrent sequence Un (having U0 = 0). The Cholesky factorization for the symmetric matrix associated to Un is also obtained.
منابع مشابه
Direct and Incomplete Cholesky Factorizations with Static Supernodes
Introduction Incomplete factorizations of sparse symmetric positive definite (SSPD) matrices have been used to generate preconditioners for various iterative solvers. These solvers generally use preconditioners derived from the matrix system, , in order to reduce the total number of iterations until convergence. In this report, we investigate the findings of ref. [1] on their method for computi...
متن کاملOn Evaluating Parallel Sparse Cholesky Factorizations
Though many parallel implementations of sparse Cholesky factorization with the experimental results accompanied have been proposed, it seems hard to evaluate the performance of these factorization methods theoretically because of the irregular structure of sparse matrices. This paper is an attempt to such research. On the basis of the criteria of parallel computation and communication time, we ...
متن کاملSVD Factorization for Tall-and-Fat Matrices on Map/Reduce Architectures
We demonstrate an implementation for an approximate rank-k SVD factorization, combiningwell-known randomized projection techniques with previously implemented map/reduce solutions in order to compute steps of the random projection based SVD procedure, such QR and SVD. We structure the problem in a way that it reduces to Cholesky and SVD factorizations on k× k matrices computed on a single machi...
متن کاملLocalization of Matrix Factorizations
Matrices with off-diagonal decay appear in a variety of fields in mathematics and in numerous applications, such as signal processing, statistics, communications engineering, condensed matter physics, and quantum chemistry. Numerical algorithms dealing with such matrices often take advantage (implicitly or explicitly) of the empirical observation that this off-diagonal decay property seems to b...
متن کاملRational and Polynomial Matrices
where λ = s or λ = z for a continuousor discrete-time realization, respectively. It is widely accepted that most numerical operations on rational or polynomial matrices are best done by manipulating the matrices of the corresponding descriptor system representations. Many operations on standard matrices (such as finding the rank, determinant, inverse or generalized inverses, nullspace) or the s...
متن کامل