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An Outline of the Problems
Linear Equations and Inequalities
Systems of Equations With Positive Definite Symmetric
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absolute value algebraic algorithm approximation arithmetic becomes boundary conditions boundary value problems Chapter Chebyshev Chebyshev Polynomials Cholesky decomposition coefficient matrix column component convergence denotes derivatives determined diagonal elements difference Editors eigenvalues eigenvectors equa Euler Euler's method exact solution example exchange step factor Figure finite formula function values given hence initial conditions interval iteration Jacobi method least squares problem linear system Math Mathematics maximum minimum Newton's method nodes nonlinear Note Numerical Analysis numerical computation numerical solution obtains operator Ordinary Differential Equations orthogonal perturbation pivot element polynomial of degree positive definite Proof qd-row quadratic form reduced remark root rounding errors Runge-Kutta methods Rutishauser scheme sequence solved spline symmetric matrix system of equations tableau Theorem tion transformation trapezoidal rule variables vector xk+i y*+i yields yk+i zero