scholarly journals Effect of the Guess Function & Continuation Method on the Run Time of MATLAB BVP Solvers

Author(s):  
Fikri Serdar
Keyword(s):  
10.28945/3391 ◽  
2009 ◽  
Author(s):  
Moshe Pelleh

In our world, where most systems become embedded systems, the approach of designing embedded systems is still frequently similar to the approach of designing organic systems (or not embedded systems). An organic system, like a personal computer or a work station, must be able to run any task submitted to it at any time (with certain constrains depending on the machine). Consequently, it must have a sophisticated general purpose Operating System (OS) to schedule, dispatch, maintain and monitor the tasks and assist them in special cases (particularly communication and synchronization between them and with external devices). These OSs require an overhead on the memory, on the cache and on the run time. Moreover, generally they are task oriented rather than machine oriented; therefore the processor's throughput is penalized. On the other hand, an embedded system, like an Anti-lock Braking System (ABS), executes always the same software application. Frequently it is a small or medium size system, or made up of several such systems. Many small or medium size embedded systems, with limited number of tasks, can be scheduled by our proposed hardware architecture, based on the Motorola 500MHz MPC7410 processor, enhancing its throughput and avoiding the software OS overhead, complexity, maintenance and price. Encouraged by our experimental results, we shall develop a compiler to assist our method. In the meantime we will present here our proposal and the experimental results.


2014 ◽  
Vol 24 (12) ◽  
pp. 2767-2781
Author(s):  
Hao SUN ◽  
Hui-Peng LI ◽  
Qing-Kai ZENG
Keyword(s):  

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.


2021 ◽  
Vol 17 (3) ◽  
pp. 1-38
Author(s):  
Ali Bibak ◽  
Charles Carlson ◽  
Karthekeyan Chandrasekaran

Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and Röglin (ACM Transactions on Algorithms, 2017) showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei (STOC, 2017) showed that the smoothed complexity of FLIP for max-cut in complete graphs is ( O Φ 5 n 15.1 ), where Φ is an upper bound on the random edge-weight density and Φ is the number of vertices in the input graph. While Angel, Bubeck, Peres, and Wei’s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress toward improving the run-time bound. We prove that the smoothed complexity of FLIP for max-cut in complete graphs is O (Φ n 7.83 ). Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for MAX-3-CUT in complete graphs is polynomial and for MAX - k - CUT in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest toward showing smoothed polynomial complexity of FLIP for MAX - k - CUT in complete graphs for larger constants k .


2021 ◽  
Vol 20 (3) ◽  
pp. 1-25
Author(s):  
Elham Shamsa ◽  
Alma Pröbstl ◽  
Nima TaheriNejad ◽  
Anil Kanduri ◽  
Samarjit Chakraborty ◽  
...  

Smartphone users require high Battery Cycle Life (BCL) and high Quality of Experience (QoE) during their usage. These two objectives can be conflicting based on the user preference at run-time. Finding the best trade-off between QoE and BCL requires an intelligent resource management approach that considers and learns user preference at run-time. Current approaches focus on one of these two objectives and neglect the other, limiting their efficiency in meeting users’ needs. In this article, we present UBAR, User- and Battery-aware Resource management, which considers dynamic workload, user preference, and user plug-in/out pattern at run-time to provide a suitable trade-off between BCL and QoE. UBAR personalizes this trade-off by learning the user’s habits and using that to satisfy QoE, while considering battery temperature and State of Charge (SOC) pattern to maximize BCL. The evaluation results show that UBAR achieves 10% to 40% improvement compared to the existing state-of-the-art approaches.


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