Numerical AnalysisProvides an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. This book focuses on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. |
Contents
Mathematical Preliminaries and Error Analysis | 1 |
Solutions of Equations in One Variable | 45 |
Interpolation and Polynomial Approximation | 101 |
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Common terms and phrases
a₁ a²u actual error actual solution y(t Algorithm approximate the solution b₁ boundary-value problem coefficients compute constant convergence cubic spline defined derivative determine diagonal differential equation eigenvalues eigenvector endpoints entries error bound Euler's method Example EXERCISE SET f(xo Figure formula function ƒ xo Gauss-Seidel Gauss-Seidel method Gaussian elimination given gives initial approximation initial-value problems integral interpolating polynomial interval least squares linear system Maple matrix Newton's method nodes norm number of iterations obtained OUTPUT P₁ polynomial of degree positive definite procedure quadrature Repeat Exercise requires round-off error Runge-Kutta method Secant method Section sequence Simpson's rule solve Step 1 Set subroutine Suppose symmetric Table Taylor polynomial technique Theorem ti+1 Trapezoidal rule tridiagonal truncation error values vector w₁ Wi+1 x₁ y₁ zero