Numerical methods using MATLAB
This book provides a fundamental introduction to numerical analysis. This book covers numerous topics including Interpolation and Polynomial Approximation, Curve Fitting, Numerical Differentiation, Numerical Integration, and Numerical Optimization. For engineering and computer science fields.
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Solution of Nonlinear Equations
Solution of Linear Systems AX B
Interpolation and Polynomial
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abscissas accuracy Algorithms and Programs Assume Bernstein polynomials Bezier curve Boole's rule boundary conditions boundary values calculations Chebyshev coefficients column compute construct converges cubic spline data points decimal places determine diagonal differential equations digits eigenpair eigenvalues eigenvector endpoints equally spaced error bound error term Euler's method evaluations Example Exercises fixed point fixed-point iteration formula function f(x function values Gaussian elimination given graph grid Hence Heun's method Input integral interpolation interval Lagrange polynomial least-squares linear system MATLAB matrix method of order minimum multiplication Newton polynomial Newton-Raphson Newton's method nodes obtain Pn(x polynomial of degree quadratic quadrature real number result root Runge-Kutta method secant method sequence Show shown in Figure Simpson's rule solve step size h subintervals substitution Suppose Table Taylor polynomial Theorem trapezoidal rule tridiagonal upper-triangular value problem variables vector zero