In theory of approximations, the classic methods of polynomial approximation for rational expression are various interpolations and operator approximations, such as Lagrange interpolation, Hermite interpolation and Bernstein polynomial approximation.

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As a result, we have demonstrated that the best approximating operator and the best approximating of bounded linear operator in H10 and H1a,+∞ are consistent and, at the same time, we have generalized the theorem of the best approximating of bounded linear operator to the more universal H1

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This is an untouched measuring way. The cameras are calibrated in the way of RAC two steps, first. With the polynomial interpolation, the pictures catched from the steel plate are treated to detect the edge in subpixel with a cross window arithmetic operators, which can fit non uniform illumination, keep the edge character and do filter in a better way. Three-dimensional scenery could be rebuilt from the two-dimensional pictures with the methods of least square fitting and contradictorily clairvoyance. Thus, the distance and its variance of two points in the given position of the plate can be achieved. It is expected that this study can provide a new and useful tool to the research on the theory of distortion of line heating.

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The main research aspects are as following. 1. The zero-order differential operator is constructed, based on the inside interpolation collocation method.

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This thesis carries on research to a class of nonlinear Schrodinger Equation with wave operator of initial value periodic problem.

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The main content includes that the accuracy of interpolation operators is creased since defect equations introduce less error: Gauss-Seidel solution can save effectively the computational time, in particular, the CPU-time for the setup phase; Jacobi-relaxation interpolation contributes to efficient and robust algebraic multigrid methods by a simple and purely algebraic mean.

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This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

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Then the interpolation representations of fuzzy controllers with Mamdani implication operator, algebra product implication operator, Zadeh implication operator and implication operator are introduced separately.

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Boolean sum projection, P〓P〓, interpolates to a primitive function f along lines; it is a transfinite interpolant.

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This operator has more detecting ability than the classical two points inner interpolative operator.

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