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Parida, P.K.,Gupta, D.K.,Parhi, S.K. The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.3
The semilocal convergence of a third order iterative method used for solving nonlinear operator equations in Banach spaces is established by using recurrence relations under the assumption that the second Fr´echet derivative of the involved operator satisfies the ${\omega}$-continuity condition given by $||F^{\prime\prime}(x)-F^{\prime\prime}(y)||{\leq}{\omega}(||x-y||)$, $x,y{\in}{\Omega}$, where, ${\omega}(x)$ is a nondecreasing continuous real function for x > 0, such that ${\omega}(0){\geq}0$. This condition is milder than the usual Lipschitz/H$\ddot{o}$lder continuity condition on $F^{\prime\prime}$. A family of recurrence relations based on two constants depending on the involved operator is derived. An existence-uniqueness theorem is established to show that the R-order convergence of the method is (2+$p$), where $p{\in}(0,1]$. A priori error bounds for the method are also derived. Two numerical examples are worked out to demonstrate the efficacy of our approach and comparisons are elucidated with a known result.
Probabilistic Spherical Detection and VLSI Implementation for Multiple-Antenna Systems
Park, C.S.,Parhi, K.K.,Sin-Chong Park IEEE 2009 IEEE transactions on circuits and systems. a publi Vol.56 No.3
<P>This paper presents a novel probabilistic spherical-detection (P-SD) method which applies the probabilistic-search algorithm to conventional depth-first SD (DF-SD). By confining the tree search into candidates which can be selected in an adaptive manner, a large number of promising candidates can be evaluated before termination. Consequently, the proposed P-SD improves the error performance of DF-SD with early termination, while retaining the hardware efficiency. An efficient VLSI architecture is proposed for implementation of the P-SD algorithm, and the results of the synthesized architecture are presented. The main advantage of P-SD is that it can fully exploit the state-of-the-art architectures of DF-SD, since it can be implemented by simply adding two functional blocks to conventional DF-SD. By analyzing the performance-complexity tradeoffs, it is concluded that our proposed P-SD is advantageous over conventional DF-SD and <I>K</I>-best algorithm, when the maximum-likelihood error performance is desired.</P>
P. Parida,D.K. Gupta,S.K. Parhi 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.3
The semilocal convergence of a third order iterative methodused for solving nonlinear operator equations in Banach spaces is establishedby using recurrence relations under the assumption that the secondFr´echet derivative of the involved operator satisfies the !-continuity conditiongiven by ∥F′′(x) − F′′(y)∥ ≤ ω(∥x − y∥), x, y ∈ Ω, where, ω(x) is anondecreasing continuous real function for x > 0, such that ω(0) ≥ 0. Thiscondition is milder than the usual Lipschitz/H¨older continuity conditionon F′′. A family of recurrence relations based on two constants dependingon the involved operator is derived. An existence-uniqueness theorem isestablished to show that the R-order convergence of the method is (2+p),where p ∈ (0, 1]. A priori error bounds for the method are also derived. Two numerical examples are worked out to demonstrate the efficacy of ourapproach and comparisons are elucidated with a known result.