99 research outputs found
Optimal parameter for the SOR-like iteration method for solving the system of absolute value equations
The SOR-like iteration method for solving the absolute value equations~(AVE)
of finding a vector such that with is investigated. The convergence conditions of the SOR-like iteration method
proposed by Ke and Ma ([{\em Appl. Math. Comput.}, 311:195--202, 2017]) are
revisited and a new proof is given, which exhibits some insights in determining
the convergent region and the optimal iteration parameter. Along this line, the
optimal parameter which minimizes with and the approximate optimal parameter which
minimizes are explored.
The optimal and approximate optimal parameters are iteration-independent and
the bigger value of is, the smaller convergent region of the iteration
parameter is. Numerical results are presented to demonstrate that the
SOR-like iteration method with the optimal parameter is superior to that with
the approximate optimal parameter proposed by Guo, Wu and Li ([{\em Appl. Math.
Lett.}, 97:107--113, 2019]). In some situation, the SOR-like itration method
with the optimal parameter performs better, in terms of CPU time, than the
generalized Newton method (Mangasarian, [{\em Optim. Lett.}, 3:101--108, 2009])
for solving the AVE.Comment: 23 pages, 7 figures, 7 table
The Optimization and Mathematical Modeling of Quality Attributes of Parboiled Rice Using a Response Surface Method
The response surface methodology was used to optimize the hydrothermal processing conditions based on the rice quality parameters of the Rong Youhua Zhan rice variety (Indica). The effect of soaking temperature (29.77, 40, 55, 70, and 80.23°C), soaking time (67.55, 90, 120, 150, and 170.45 min), and steaming time (1.59, 5, 10, 15, and 18.41 min), each tested at five levels, on percentage of head rice yield (HRY), hardness, cooking time, lightness, and color were determined, with R2 values of 0.96, 0.94, 0.90, 0.88, and 0.94, respectively. HRY, hardness, cooking time, and color increased with process severity while lightness decreased, although HRY decreased after reaching a maximum. The predicted optimum soaking temperature, soaking time, and steaming time were 69.88°C, 150 min, and 6.73 min, respectively, and the predicted HRY, hardness, cooking time, lightness, and color under these conditions were 73.43%, 29.95 N, 32.14 min, 83.03 min, and 12.24 min, respectively, with a composite desirability of 0.9658. The parboiling industry could use the findings of the current study to obtain the desired quality of parboiled rice. This manuscript will be helpful for researchers working on commercializing parboiled rice processes in China as well as in other countries
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