Youtor
Successive Over Relaxation SOR Iteration method How to solve linear system of algebraic equations
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SOR Method to Solve system of Linear Equations| Numerical Analysis • In theoretical terms, the Successive Over-Relaxation (SOR) method is an iterative technique used to solve systems of linear equations Ax=B. It is based on the concept of successive approximations to the solution vector x The SOR method aims to find the solution vector x. by updating its components iteratively until a desired level of accuracy is achieved. Here's how the SOR method works theoretically: • Initialization: Start with an initial guess for the solution vector x^(0) • Iteration: At each iteration k update the components of x according to the SOR formula: • Where: • x^(k+1) is the i-th component of the solution vector at the k+1-th iteration • Convergence: Iterate until the solution converges to within a specified tolerance or until a maximum number of iterations is reached. • The convergence of the SOR method depends on the choice of the relaxation factor w. if w=1 the SOR method reduces to the Gauss-Seidel method. An optimal value of w can accelerate convergence compared to Gauss-Seidel, but choosing it too large can lead to instability. The optimal value of depends on the specific problem being solved and often requires empirical or theoretical analysis. • In theoretical discussions, the SOR method is analyzed for convergence properties, such as convergence rate, stability, and conditions for convergence. These analyses often involve techniques from numerical analysis, such as matrix norms, spectral radius, and convergence theorems. • Hashtags • #linearequations #linearequationsintwovariablesclass10 #linearequationsintwovariablesclass9 #linearequationsinonevariableclass8 #linearequationswordproblems #linearequationsintwovariablesclass8 #linearequationsinonevariableclass7 #linearequationsclass8 #linearequationsgrade9 #linearequationsclass6 #linearequationsintwovariablesclass10oneshot #linearequationsintwovariablesclass10importantquestions #linearequationsgrade8 #linearequationsclass10 #linearequationsclass9 #linearequationsand #linearequationsandinequalitiesclass9 #linearequationsandrationalequations #linearequationsandinequalitiesclass7 #linearequationsandlinearsystems #linearequationsandinequalitiesclass8 #linearequationsandquadraticequations #linearequationsandinequalitiesinonevariableclass8icse #linearequationsandtheirapplications #linearequationsandapplications #linearequationsandinequalitiesclass11 #linearequationsandinequalitiesintwovariablesclass104.1 #linearequationsandsolutions #linearequationsandproblemsolving #linearequationsandinequalitiesclass8icse • #sormethod #sormethodand • channel link • https://youtube.com/@expertmathematic... • For Notes: Contact on 0317-7665396 • playlist link: • • tags • sor,successive over-relaxation
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