Abstract: Newton-Lagrange Interpolations are widely used in
numerical analysis. However, it requires a quadratic computational
time for their constructions. In computer aided geometric design
(CAGD), there are some polynomial curves: Wang-Ball, DP and
Dejdumrong curves, which have linear time complexity algorithms.
Thus, the computational time for Newton-Lagrange Interpolations
can be reduced by applying the algorithms of Wang-Ball, DP and
Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong
algorithms, first, it is necessary to convert Newton-Lagrange
polynomials into Wang-Ball, DP or Dejdumrong polynomials. In
this work, the algorithms for converting from both uniform and
non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and
Dejdumrong polynomials are investigated. Thus, the computational
time for representing Newton-Lagrange polynomials can be reduced
into linear complexity. In addition, the other utilizations of using
CAGD curves to modify the Newton-Lagrange curves can be taken.
Abstract: In this paper, we presented not only development technology of an explosion proof type and portable combustible gas leak detector but also algorithm to improve accuracy for measuring gas concentrations. The presented techniques are to apply the flame-proof enclosure and intrinsic safe explosion proof to an infrared gas leak detector at first in Korea and to improve accuracy using linearization recursion equation and Lagrange interpolation polynomial. Together, we tested sensor characteristics and calibrated suitable input gases and output voltages. Then, we advanced the performances of combustible gaseous detectors through reflecting demands of gas safety management fields. To check performances of two company's detectors, we achieved the measurement tests with eight standard gases made by Korea Gas Safety Corporation. We demonstrated our instruments better in detecting accuracy other than detectors through experimental results.
Abstract: In this era of online communication, which transacts data in 0s and 1s, confidentiality is a priced commodity. Ensuring safe transmission of encrypted data and their uncorrupted recovery is a matter of prime concern. Among the several techniques for secure sharing of images, this paper proposes a k out of n region incrementing image sharing scheme for color images. The highlight of this scheme is the use of simple Boolean and arithmetic operations for generating shares and the Lagrange interpolation polynomial for authenticating shares. Additionally, this scheme addresses problems faced by existing algorithms such as color reversal and pixel expansion. This paper regenerates the original secret image whereas the existing systems regenerates only the half toned secret image.
Abstract: In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.