• Title/Summary/Keyword: iteration numbers

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REPULSIVE FIXED-POINTS OF THE LAGUERRE-LIKE ITERATION FUNCTIONS

  • Ham, YoonMee;Lee, Sang-Gu
    • Korean Journal of Mathematics
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    • v.16 no.1
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    • pp.51-55
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    • 2008
  • Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixed-point of an iteration function is a fixed-point different from a zero of f. We prove that all extraneous fixed-points of Laguerre-like iteration functions and general Laguerre-like functions are repulsive.

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ITERATION OF 2 × 2 MATRICES IN ℤ4 AND THEIR FOUR COLOR EXPRESSIONS (I)

  • DAEYEOUL KIM
    • Journal of Applied and Pure Mathematics
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    • v.6 no.1_2
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    • pp.37-45
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    • 2024
  • The aim of this article is to consider the sequences generated by repeatedly performing matrix multiplication operations, define the stable, amicable pair, sociable matrix sequences, and analyze the results obtained through iteration. Lastly, numbers are changed to colors to make them easier to understand.

Performance Enhancement of CORDIC Employing Redundant Numbers and Minimal Iterations (잉여 수와 최소 반복 횟수를 이용한 CORDIC 성능 향상)

  • Kim, Seung-Youl;You, Young-Gap
    • The Journal of the Korea Contents Association
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    • v.6 no.2
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    • pp.162-168
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    • 2006
  • This paper presents a high performance CORDIC circuit based on redundant numbers yielding a minimal number of iteration stages. The minimal number of iteration stages reflects the iteration number yielding a smaller computation error than the truncation error. The minimal number of iterations is found n-4 for $n\geq16$, where n is the number of input angle bits. The CORDIC circuit is based on a redundant number system with a constant scale factor The circuit performs sine and cosine calculations with a delay of {5 (n-4)+ 2[$log_{2}n$]}$\DeltaT$.

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Generalized Joint Channel-Network Coding in Asymmetric Two-Way Relay Channels

  • Shen, Shengqiang;Li, Shiyin;Li, Zongyan
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.10 no.12
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    • pp.5361-5374
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    • 2016
  • Combining channel coding and network coding in a physical layer in a fading channel, generalized joint channel-network coding (G-JCNC) is proved to highly perform in a two-way relay channel (TWRC). However, most relevant discussions are restricted to symmetric networks. This paper investigates the G-JCNC protocols in an asymmetric TWRC (A-TWRC). A newly designed encoder used by source nodes that is dedicated to correlate codewords with different orders is presented. Moreover, the capability of a simple common non-binary decoder at a relay node is verified. The effects of a power match under various numbers of iteration and code lengths are also analyzed. The simulation results give the optimum power match ratio and demonstrate that the designed scheme based on G-JCNC in an A-TWRC has excellent bit error rate performance under an appropriate power match ratio.

The performance estimation of Channel coding schemes in Wideband Code Division Multiple Access System with fading channel (페이딩 환경의 W-CDMA에서 채널부호화 방식의 성능평가)

  • 이종목;심용걸
    • Proceedings of the IEEK Conference
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    • 2000.11a
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    • pp.165-168
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    • 2000
  • The bit error rate(BER)of the data passed through Wideband-Code Division Multiple Access (W-CDMA) system with turbo-codes structure is presented. The performance of turbo-codes under W-CDMA system is estimated for various users and iteration numbers of decoding. The channel model is Additive White Gaussian Noise(AWGN) and Rayleigh fading channel. When iteration number increases, bit error probability of turbo-codes decreases. and when the number of users increase, bit error probability of turbo-codes increases.

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The Three-step Intermixed Iteration for Two Finite Families of Nonlinear Mappings in a Hilbert Space

  • Suwannaut, Sarawut;Kangtunyakarn, Atid
    • Kyungpook Mathematical Journal
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    • v.62 no.1
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    • pp.69-88
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    • 2022
  • In this work, the three-step intermixed iteration for two finite families of nonlinear mappings is introduced. We prove a strong convergence theorem for approximating a common fixed point of a strict pseudo-contraction and strictly pseudononspreading mapping in a Hilbert space. Some additional results are obtained. Finally, a numerical example in a space of real numbers is also given and illustrated.

Power Line Noise Reductions in ABR by Properly Chosen Iteration Numbers (ABR에서 반복회수 설정에 의한 전력선 잡음의 제거)

  • 안주현;김수찬;남기창;심윤주;김희남;송철규;김덕원
    • Journal of Biomedical Engineering Research
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    • v.22 no.3
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    • pp.241-247
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    • 2001
  • ABR(auditory brainstem response) is one of the audiometry which measures objective hearing threshold level by acquiring electric evoked potentials emanated from auditory nerve system responding to an auditory stimulation. However, the obtained potentials which are largely interfered by power line noise, have extremely low SNR, thus ensemble average algorithm is generally used. The purpose of this study was to investigate the effect of iteration number in ensemble average on the reduction of the power line noise. The power line noise was modeled to be a 60 Hz sinusoidal signal and the energy of the modeled signal was calculated when it was averaged. It was verified by simulation that the energy had the periodic zero points for each stimulation rate, and 60 Hz signal induced by the power line was applied to the developed ABR system to confirm that the period of zero energy point was the same with that of the simulation. By the properly selected iteration number, power line noise could be reduced and more reliable ABR could be acquired.

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Nonlinear Wave Interaction of Three Stokes' Waves in Deep Water: Banach Fixed Point Method

  • Jang, Taek-S.;Kwon, S.H.;Kim, Beom-J.
    • Journal of Mechanical Science and Technology
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    • v.20 no.11
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    • pp.1950-1960
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    • 2006
  • Based on Banach fixed point theorem, a method to calculate nonlinear superposition for three interacting Stokes' waves is proposed in this paper. A mathematical formulation for the nonlinear superposition in deep water and some numerical solutions were investigated. The authors carried out the numerical study with three progressive linear potentials of different wave numbers and succeeded in solving the nonlinear wave profiles of their three wave-interaction, that is, using only linear wave potentials, it was possible to realize the corresponding nonlinear interacting wave profiles through iteration of the method. The stability of the method for the three interacting Stokes' waves was analyzed. The calculation results, together with Fourier transform, revealed that the iteration made it possible to predict higher-order nonlinear frequencies for three Stokes' waves' interaction. The proposed method has a very fast convergence rate.

A Study on High Speed LDPC Decoder Based on HSS (HSS기반의 고속 LDPC 복호기 연구)

  • Jung, Ji Won
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.5 no.3
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    • pp.164-168
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    • 2012
  • LDPC decoder architectures are generally classified into serial, parallel and partially parallel architectures. Conventional method of LDPC decoding in general give rise to a large number of computation operations, mass power consumption, and decoding delay. It is necessary to reduce the iteration numbers and computation operations without performance degradation. This paper studies Horizontal Shuffle Scheduling (HSS) algorithm. In the result, number of iteration is half than conventional algorithm without performance degradation. Finally, this paper present design methodology of high-speed LDPC decoder and confirmed its throughput is up to about 600Mbps.

A study on the accuracy of a numerical iteration for Markov processes by using reliability models (신뢰도 모형을 이용한 마코프 과정의 수치적 반복법의 정확성에 대한 연구)

  • Hyeonah Park;Seongryong Na
    • The Korean Journal of Applied Statistics
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    • v.37 no.4
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    • pp.445-453
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    • 2024
  • For Markov processes whose stationary probabilities are difficult to obtain in the analytical form, approximate solutions can be considered using numerical methods such as a matrix operation method or an iterative calculation method. In this paper we perform the study to verify the accuracy of a numerical iteration formula which calculate the stationary probabilities of Markov chains or processes. Especially, the convergence and accuracy of the numerical method are investigated by using Markov models for system availability. We compare the values of the system availability based on the numerical calculation and those based on the complicated but analytical solutions. We also calculate the iteration numbers necessary for the convergence of the numerical solutions. The accuracy and usefulness of the numerical iterative calculation method can be ascertained through this study.