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System of linear equation 1-1 | linear equation | ![]() |
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System of linear equation 1-2 | linear equation | ![]() |
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System of linear equation 2 | linear equation, condition number | ![]() |
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System of linear equation 3-1 | Posteriori analysis, Lu factorization | ![]() |
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System of linear equation 3-2 | Lu factorization, Pivoting | ![]() |
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Special types of matrices | Cholesky factorization | ![]() |
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Linear least square1 | least square, normal equation | ![]() |
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Linear least square2 | least square, QR decomposition | ![]() |
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Linear least square3 (SVD) | Singular Value Decomposition (SVD) | ![]() |
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Linear least square4 (SVD) | Pseudo-Inverse, Rank deficient least square | ![]() |
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Linear least square5 | Householder transformation, Given rotation | ![]() |
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Iterative methods | iterative method | ![]() |
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Iterative methods2 | Jacobi method, Gauss-Seidal method | ![]() |
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Iterative methods3 | SOR(Successive overrelaxation), Gradient method | ![]() |
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Iterative methods4 | Gradient method | ![]() |
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Iterative method5 | Conjugate gradient method | ![]() |
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Iterative method6 | Generalize of Conjugate gradient mehtod | ![]() |
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Eigenvalue problem1 | eigenvalue decomposition, algebraic multiplication, geometric multiplication | ![]() |
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Eigenvalue problem2 | Schur canonical form, Schurs unitary triangularization, Gershgorin | ![]() |
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Eigenvalue problem3 | Power iteration, Inverse iteration | ![]() |
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Eigenvalue problem4 | Orthogonal iteration, QR iteration | ![]() |
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Eigenvalue problem5 | Upper Hessenberg form | ![]() |
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Eigenvalue problem6 | Rayleigh-Ritz quotient | ![]() |
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Nonlinear equations1 | Sensitivity & conditioning, Bisection method | ![]() |
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Nonlinear equations2 | Newton method, secant method, contrative mapping thm | ![]() |
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Nonlinear equations3 | Quadratic convergence of newton method, Broydens method | ![]() |
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Nonlinear equations4 | Fixed pt method | ![]() |
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Optimization1 | Existence & Uniqueness, Optimization in 1-D | ![]() |
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Optimization2 | line search method, trast region method, armijo condition, curvature condition, back tracking method | ![]() |
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Optimization3 | Quasi-Newton method, Secant-like method, BFGS method | ![]() |
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Optimization4 | Nonlinear least square, newton method, gauss-newton method, constrained optimization, feasible direction, lagrangian function | ![]() |
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Optimization5 , Interpolation1 | Penalty method, Barrier method, polynomial interpolation, monimial basis, horners method | ![]() |
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Interpolation2 | Lagrange interpolation, Newton interpolation | ![]() |
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Interpolation3 | Runges counter example, Cubic spline interpolation | ![]() |
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Interpolation4, Numerical integration1 | ![]() |