A minimizing algorithm of solving large-scale sparse normal equation
Liu Zuan-wu
Abstract
Liu Zuan-wu
Abstract
Aiming at the difficulties of solving large-scale normal equation and error equation,it proposes a method on the basis of Cholesky decomposition principle.A good sequence for matrix is arranged,and the triangular matrices for Cholesky decomposition contain less non-zero elements.The structured decomposition of symmetric matrices is introduced,and the seats and numbers of non-zero elements of triangular matrix will be determined.The store places will be distributed in advance,and the numerical solution can be calculated on the seats of non-zero elements.Lastly,the related methods and the numerical results are given.
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Aiming at the difficulties of solving large-scale normal equation and error equation,it proposes a method on the basis of Cholesky decomposition principle.A good sequence for matrix is arranged,and the triangular matrices for Cholesky decomposition contain less non-zero elements.The structured decomposition of symmetric matrices is introduced,and the seats and numbers of non-zero elements of triangular matrix will be determined.The store places will be distributed in advance,and the numerical solution can be calculated on the seats of non-zero elements.Lastly,the related methods and the numerical results are given.
Key concepts: Cholesky decomposition, Minimum degree algorithm, Triangular matrix, Matrix (chemical analysis), Zero (linguistics), Decomposition, LU decomposition, Scale (ratio)