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The Squareroot Method
Partitioning into SubMatrices
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absolute magnitude accuracy approximate solution arbitrary boundary conditions boundary nodes boundary value problem calculations Cauchy problem characteristic polynomial coefficients column Consequently consider constant convergence corresponding defined derivatives difference equation difference methods difference scheme differential equations Dirichlet problem eigen eigenvalues eigenvectors equal error estimate exact solution find the solution first-order formula function Goursat problem initial conditions integral equation internal nodes interval iteration linear algebraic linear algebraic equations linear combination linearly independent matrix mesh method method of solving multiplied non-zero norm obtained operator orthogonal Poisson's equation positive definite presupposed real roots required to find right-hand side satisfies the initial sequence set of equations set of linear solution of eqn straight line Substituting successive approximation Suppose we put symmetric symmetric matrix Taylor formula theorem vector c0 whilst xv x2 zero