Newton’s method for the matrix square root
نویسندگان
چکیده
منابع مشابه
Newton's Method for the Matrix Square Root*
One approach to computing a square root of a matrix A is to apply Newton's method to the quadratic matrix equation F( X) = X2 A =0. Two widely-quoted matrix square root iterations obtained by rewriting this Newton iteration are shown to have excellent mathematical convergence properties. However, by means of a perturbation analysis and supportive numerical examples, it is shown that these simpl...
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The Schur method for computing a matrix square root reduces the matrix to the Schur triangular form and then computes a square root of the triangular matrix. We show that by using either standard blocking or recursive blocking the computation of the square root of the triangular matrix can be made rich in matrix multiplication. Numerical experiments making appropriate use of level 3 BLAS show s...
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Two-particle scattering amplitudes for integrable relativistic quantum field theory in 1+1 dimensions can normally have at most singularities of poles and zeros along the imaginary axis in the complex rapidity plane. It has been supposed that single particle amplitudes of the exact boundary reflection matrix exhibit the same structure. In this paper, single particle amplitudes of the exact boun...
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We generalize a “one eigenstate” theorem of Levy, Perdew and Sahni (LPS) [1] to the case of densities coming from eigenmixture density operators. The generalization is of a special interest for the radial density functional theory (RDFT) for nuclei [2], a consequence of the rotational invariance of the nuclear Hamiltonian; when nuclear ground states (GSs) have a finite spin, the RDFT uses eigen...
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A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and division operations in the QRD normalization and backward substitution steps in the LS computations. It is claimed in [1] that the LS solution only requires ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1986
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1986-0829624-5