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Solution of Linear Systems of Equations
The Algebraic Eigenvalue Problem
18 other sections not shown
algorithm applied approximation assume calculate called Chebyshev Chebyshev polynomials coefficient matrix column component consider constant CONTINUE convergence cubic spline defined denote derivative diagonal differential equations eigenvalues eigenvectors entries equally spaced estimate Euler's method evaluate example function Gauss elimination given Hence Hessenberg Hessenberg matrix initial guess initial-value problem inner product integral interpolating polynomial interval inverse power method Jacobi method least-squares linear system linearly independent matrix norms multiplications multistep methods n x n Newton's method nonsingular nonzero norm obtain one-step method orthogonal orthonormal precision procedure proof relative error root Runge-Kutta method satisfies scalar secant method Section sequence Simpson's rule solution solve step size h subroutine suppose symmetric Taylor's series technique Theorem tion trapezoidal rule triangular truncation error values vector verify yields zeros