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The rate of convergence of the coefficient matrix with condition number as compared with the condition number of the Hilbert matrix H is provided with respect to the infinity norm, i.e., R_{infty} = frac{C_{infty}(A)}{C_{infty}(H }, that (C_{infty}(A) := operatorname{Cond}_{infty}(A)).
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Also it should be noted that the matrices with conditions (4) and (6) belong to the class O 1 -.
Moreover the drawbacks rising from the poor selection of shape parameter and also the full resultant matrix with high condition number are reduced.
A series of solid nanocomposites containing CdS nanoparticles in polymeric matrix with varied conditions on the interface particle/polymer was fabricated and studied by photoluminescence (PL) and optically detected magnetic resonance (ODMR) methods.
In Section 5.3.2, we, however, investigate the influence of various input matrices with different condition numbers on the algorithm's performance.
From the previous theorem it immediately follows that, for (b=0), we obtain symmetric stiffness matrices with small condition numbers which are independent of ϵ and are dependent only on Riesz constants of the used wavelet basis.
The matrix with the lowest condition number (i.e. the best-conditioned) was selected as the basis matrix to be used for deconvolution.
A constituted matrix with a smaller condition number responds better to design targets.
The problem of how a two-dimensional synaptic matrix with periodic boundary conditions, postulated to underlie grid cell behaviour, could be self-organized in early development is addressed.
In case B is a real symmetric matrix with some additional conditions attached to its elements, and by using variational approaches (see [8]), this paper presents the existence criteria for the positive and negative solutions of (1).
We present an O(max(n, nm)) algorithm for generating a random matrix with the above conditions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com