(BQ) Part 2 book "Applied numerical methods" has contents: Linear regression, fourier analysis, polynomial interpolation, splines and piecewise interpolation, numerical integration formulas, numerical integration of functions, numerical differentiation, boundary value problems,...and other contents.
(BQ) Part 2 book "Applied numerical methods with MATLAB for engineers and scientists" has contents: Matrix inverse and condition, matrix inverse and condition, eigenvalues, linear regression, polynomial interpolation, numerical integration formulas,...and other contents.
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
10.1 10.2 10.3 10.4 Introduction Polynomial Interpolation Model-Based Interpolation Summary
nterpolation is the estimation of the unknown, or the lost, samples of a signal using a weighted average of a number of known samples at the neighbourhood points. Interpolators are used in various forms in most signal processing and decision making systems.
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)
Chương 4 - Các phương pháp cho hàm rời rạc. Chương này trình bày về đa thức nội suy (Polynomial interpolation) và phương pháp bình phương tối thiểu. Nội dung cụ thể gồm có: Nội suy Lagrangian, nội suy Newton, nội suy bậc 3 (Cubic spline interpolation), làm khớp dữ liệu cho các hàm tuyến tính, làm khớp dữ liệu cho các hàm phi tuyến.
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
Computers are one of the most important tools in any field of science and
especially in physics. A student in an undergraduate lab will appreciate the
help of a computer in calculating a result from a series of measurements.
The more advanced researcher will use them for tasks like simulating an
experiment, or solving complex systems of equations. Physics is deeply
connected to mathematics and requires a lot of calculational skills. If one is
only interested in a conceptual understanding of the field, or an estimate of
the outcome of an experiment, simple calculus will probably suffice.
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 Derivatives of Orthonormal Polynomials and ´ Coefﬁcients of Hermite-Fejer Interpolation
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 Interpolation Functions of q-Extensions of Apostol’s Type Euler Polynomials
(BQ) Part 1 book "Numerical analysis" has content: Mathematical preliminaries and error analysis, solutions of equations in one variable, interpolation and polynomial approximation, numerical differentiation and integration, initial value problems for ordinary differential equations, direct methods for solving linear systems.
Timing Adjustment by Interpolation
In this chapter we focus on digital interpolation and interpolator control. In Section 9.1 we discuss approximations to the ideal interpolator. We first consider FIR filters which approximate the ideal interpolator in the mean square sense. A particularly appealing solution for high rate applications will be obtained if the dependency of each filter tap coefficient on the fractional delay is approximated by a polynomial in the fractional delay. It is shown that with low-order polynomials excellent approximations are possible. In Section 9.
In this paper the spline approximation was applied to the empirical vertical profiles of oceanographic parameters such as temperature, salinity or density to obtain a more precise and reliable result of interpolation. Our experiments with the case of observed temperature profiles in Eastern Sea show that the cubic polynomial spline method has a higher reliability and precision in a comparison with the linear interpolation and other traditional methods. The method was realized as a subroutine in our programs for oceanographic data management and manipulation.
Chúng tôi cung cấp cho một cuộc khảo sát ngắn gọn trên một phương pháp tiếp cận mới trong nghiên cứu của máy chiếu đa thức bảo toàn đồng nhất một phần phương trình vi phân hoặc quan hệ khác biệt giữa đồng nhất, và các tài sản của họ suy về không gian của điều kiện suy.
(BQ) Part 2 book "MATLAB an introduction with applications" has contents: User-Defined functions and function files; polynomials, curve fitting, and interpolation; applications in numerical analysis; three dimensional plots; symbolic math.
(BQ) Part 1 book "Fundamental numerical methods and data analys" has contents: A note added for the internet edition, a further note for the internet edition, introduction and fundamental concepts, the numerical methods for linear equations and matrices, polynomial approximation, interpolation, and orthogonal polynomials.