• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.369-389
• /
• 2006

The iterative algorithms with errors for solutions to accretive operator inclusions are investigated in Banach spaces, including a modification of Rockafellar's proximal point algorithm. Some applications are given in Hilbert spaces. Our results improve the corresponding results in [1, 15-17, 29, 35].

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.771-790
• /
• 2006

The iterative algorithms with errors for nonexpansive mappings are investigated in Banach spaces. Strong convergence theorems for these algorithms are obtained. Our results improve the corresponding results in [5, 13-15, 23, 27-29, 32] as well as those in [1, 16, 19, 26] in framework of a Hilbert space.

• Communications of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.147-161
• /
• 2016

In this paper, we study the strong convergence and stability of a new two step random iterative scheme with errors for accretive Lipschitzian mapping in real Banach spaces. The new iterative scheme is more acceptable because of much better convergence rate and less restrictions on parameters as compared to random Ishikawa iterative scheme with errors. We support our analytic proofs by providing numerical examples. Applications of random iterative schemes with errors to variational inequality are also given. Our results improve and establish random generalization of results obtained by Chang [4], Zhang [31] and many others.

• Korean Journal of Mathematics
• /
• v.24 no.2
• /
• pp.181-198
• /
• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

• Communications of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.243-267
• /
• 2013

This paper is dedicated to study a new class of general nonlinear random A-maximal $m$-relaxed ${\eta}$-accretive (so called (A, ${\eta}$)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in $q$-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal $m$-relaxed ${\eta}$-accretive mappings due to Lan et al. and Chang's lemma [13], some new iterative algorithms with mixed errors for finding the approximate solutions of the aforesaid class of nonlinear random equations are constructed. The convergence analysis of the proposed iterative algorithms under some suitable conditions are also studied.

• East Asian mathematical journal
• /
• v.25 no.2
• /
• pp.141-146
• /
• 2009

In this paper, we introduce a new generalized nonlinear quasivariational inequality and establish its equivalence with a xed point problem by using the resolvent operator technique. Utilizing this equivalence, we suggest two iterative schemes, prove two existence theorems of solutions for the generalized nonlinear quasivariational inequality involving generalized cocoercive mapping and establish some convergence results of the sequences generated by the algorithms. Our results include several previously known results as special cases.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.823-834
• /
• 2007

We introduce a new system of generalized nonlinear mixed quasivariational inequalities and prove the existence and uniqueness of the solution for the system in Hilbert spaces. The main result of this paper is an extension and improvement of the well-known corresponding results in Kim-Kim [16], Noor [21]-[23] and Verma [24]-[26].

• Journal of Positioning, Navigation, and Timing
• /
• v.6 no.3
• /
• pp.105-116
• /
• 2017

Several wireless localization algorithms are evaluated for the IR-UWB-based indoor location with the assumption that the ranging measurements contain the channelwise Non-Calibration Error (NCE). The localization algorithms can be divided into the Model-free Localization (MfL) methods and Model-based Kalman Filtering (MbKF). The algorithms covered in this paper include Iterative Least Squares (ILS), Direct Solution (DS), Difference of Squared Ranging Measurements (DSRM), and ILS-Common (ILS-C) methods for the MfL methods, and Extended Kalman Filter (EKF), EKF-Each Channel (EKF-EC), EKF-C, Cubature Kalman Filter (CKF), and CKF-C for the MbKF. Experimental results show that the DSRM method has better accuracy than the other MfL methods. Also, it demands smallest computation time. On the other hand, the EKF-C and CKF-C require some more computation time than the DSRM method. The accuracy of the EKF-C and CKF-C is, however, best among the 9 methods. When comparing the EKF-C and CKF-C, the CKF-C can be easily used. Finally, it is concluded that the CKF-C can be widely used because of its ease of use as well as it accuracy.

• Korean Journal of Remote Sensing
• /
• v.34 no.6_1
• /
• pp.1143-1153
• /
• 2018

For TOPS InSAR processing, high-precision image co-registration is required. We propose an image co-registration method suitable for the TOPS mode by comparing the performance of cross correlation method, the geometric co-registration and the enhanced spectral diversity (ESD) matching algorithm based on the spectral diversity (SD) on the Sentinel-1 TOPS mode image. Using 23 pairs of interferometric pairs generated from 25 Sentinel-1 TOPS images, we applied the cross correlation (CC), geometric correction with only orbit information (GC1), geometric correction combined with iterative cross-correlation (GC2, GC3, GC4), and ESD iteration (ESD_GC, ESD_1, ESD_2). The mean of co-registration errors in azimuth direction by cross correlation and geometric matching are 0.0041 pixels and 0.0016 pixels, respectively. Although the ESD method shows the most accurate result with the error of less than 0.0005 pixels, the error of geometric co-registration is reduced to 0.001 pixels by repetition through additional cross correlation matching between the reference and resampled slave image. The ESD method is not applicable when the coherence of the burst overlap areas is low. Therefore, the geometric co-registration method through iterative processing is a suitable alternative for time series analysis using multiple SAR data or generating interferogram with long time intervals.