In the face of sparsity, statistical models are often interpolated with lower order (backoff) models, particularly in Language Modeling. In this paper, we argue that there is a relation between the higher order and the backoff model that must be satisﬁed in order for the interpolation to be effective. We show that in n-gram models, the relation is trivially held, but in models that allow arbitrary clustering of context (such as decision tree models), this relation is generally not satisﬁed. ...
Rational Function Interpolation and Extrapolation
Some functions are not well approximated by polynomials, but are well approximated by rational functions, that is quotients of polynomials. We denote by Ri(i+1)...(i+m) a rational function passing through the m + 1 points (xi , yi ) . . . (xi+m , yi+m ). More explicitly, suppose Ri(i+1)...(i+m) = p 0 + p1 x + · · · + pµ x µ Pµ (x) = Qν (x) q 0 + q 1 x + · · · + q ν xν (3.2.1)
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Block-Matching Translational and Rotational Motion Compensated Prediction Using Interpolated Reference Frame
Suppose that you have decided to use some particular interpolation scheme, such as fourth-order polynomial interpolation, to compute a function f(x) from a set of tabulated xi ’s and fi ’s. Then you will need a fast way of ﬁnding your place
Occasionally you may wish to know not the value of the interpolating polynomial that passes through a (small!) number of points, but the coefﬁcients of that polynomial. A valid use of the coefﬁcients might be, for example, to compute simultaneous interpolated values
Digital Elevation Model (DEM) is an important component of GIS applications in many socio-economic areas. Especially, DEM has a very important role in monitoring and managing natural resources, preventing natural hazards, and supporting spatial decision making. Usually, DEM is built by interpolation from a limited set of sample points. Thus, the accuracy of the DEM is depended on the used interpolation method.
Tham khảo tài liệu 'art of surface interpolation-chapter 5:solving special tasks in the next sections there are examples of interpolation problems,', công nghệ thông tin, kỹ thuật lập trình phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả
In multidimensional interpolation, we seek an estimate of y(x1 , x2 , . . . , xn ) from an n-dimensional grid of tabulated values y and n one-dimensional vectors giving the tabulated values of each of the independent variables x1 , x2, . . . , xn .
This paper analyzes the stability of linear, lumped, quadratic, and cubic spatial interpolation functions in finite element one‐dimensional kinematic wave schemes for simulation of rainfall‐runoff processes. Galerkin’s residual method transforms the kinematic wave partial
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Two-Stage Interpolation Algorithm Based on Fuzzy Logics and Edges Features for Image Zooming
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài:
Research Article Localized Mode DFT-S-OFDMA Implementation Using Frequency and Time Domain Interpolation