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Home  >  Transactions ... 2017)

9. Computing Square Root of Diagonalizable Matrix with Positive Eigenvalues and Iterative Solution to Nonlinear System of Equation: The Role of Lagrange Interpolation Formula by Stephen Ehidiamhen UWAMUSI Tran. of NAMP Vol. 5,(Sept, Nov., 2017), pp 65 – 7
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The iterative methods for solving system of nonlinear equation is presented and extension is made to include the so called SVD of a matrix for the positive eigenvalues of a matrix. By incorporating the use Lagrange interpolation formula, we are able to compute the square root of a matrix where the sign function of a matrix can be obtained cheaply. Particularly, we use the Schultz Hyper power method for approximating inverse of linear bounded operator in Hilbert space in speeding up Newton iteration for matrix square root. The discussed methods are amenable to Aerospace computation for polar decomposition for the direction matrix cosine. Details of above procedures form the peak of discussion.
Keyword: Nonlinear systems, adaptive splitting, svd, matrix square roots, lagrange interpolation, Newton iteration.