Gauss Jacobi & Gauss Seidel | Iterative Methods in Numerical Methods

In this lecture, we explore special matrices and iterative methods used in Numerical Methods for solving systems of linear equations. The video begins with an introduction to important matrix structures that frequently appear in computational mathematics. First, we discuss different types of special matrices, including tridiagonal (band) matrices, sparse matrices, and dense matrices. You will also learn how to measure the sparsity of a matrix and why sparse structures are important in numerical computation. Next, we explain important matrix properties used in iterative techniques. These include the conditions for a positive definite matrix and how to verify them. We also study diagonally dominant matrices and learn how to check whether a given matrix satisfies diagonal dominance. After building this theoretical foundation, the lecture introduces two important iterative methods for solving linear systems: • Gauss Jacobi Method – concept, working rule, and a solved example • Gauss Seidel Method – step-by-step procedure and example These methods are widely used in numerical analysis, engineering mathematics, scientific computing, and applied mathematics because they are efficient for large systems of equations, especially when dealing with sparse matrices. This lecture is useful for BS Mathematics, Engineering, Computer Science, and university students studying Numerical Methods or Linear Algebra. Watch the full lecture to clearly understand special matrices, matrix properties, and iterative techniques used in solving linear systems. 📌 Perfect for: • BS Mathematics students • Engineering students • Competitive exam preparation • Numerical Analysis learners Watch till the end for a complete understanding with theory + graphical intuition + practical examples. Subscribe to Learn with Arisha for more detailed lectures on numerical methods and MATLAB tutorials. 🔹More Playlists: ✅ Numerical Methods Quick Concepts | Short Urdu Videos https://youtube.com/playlist?list=PLQN-EgCjaCPE9hGvVPG4LWdyqYCNS-_Z4&si=aOhbAFoR1XanUrlj ✅Numerical Methods – Full Course https://youtube.com/playlist?list=PLQN-EgCjaCPEH08zW7aUvCJR-BfscRZg-&si=9NwkOOWmed6RkDX1 ✅ 3D Plotting in MATLAB | Learn with Arisha https://youtube.com/playlist?list=PLQN-EgCjaCPFKXGCIzLj-QVcvojLfJVWf&si=-JPTqK-Js0T2lfFV ✅ 2D Plotting in MATLAB | Learn with Arisha https://youtube.com/playlist?list=PLQN-EgCjaCPFUtyWcKDpCbPmcYMC8nnQC&si=McpIOs4a8rcub3Gb ✅ Numerical Analysis Complete Course https://youtube.com/playlist?list=PLQN-EgCjaCPGrYf4xZ0BhxXvPgdZ-Y9ks&si=8SB4AG9_G9CqJ_ue ✅MATLAB for Numerical Computation https://youtube.com/playlist?list=PLQN-EgCjaCPEZZQ5t6xzWn7Xxv3042bjG&si=CGwmwKr6-Dt-y4X- 🚀 Boost Your Numerical Computing Skills! This tutorial is perfect for students, engineers, and programmers who want to understand numerical errors in computational mathematics and MATLAB programming. 💡 Want More Tutorials on Numerical Methods? 👉 Subscribe for more computational math & MATLAB lessons! 👉 Hit the Like button if this video helps! 👉 Have questions? Comment below! 🔔 Stay updated with the latest programming & numerical analysis tutorials! #NewtonRaphsonMethod #NumericalMethods #EngineeringMathematics #NumericalAnalysis #RootFindingMethod #NewtonMethod #RateOfConvergence #QuadraticConvergence # Graphical Explanation #SolvedExample #MathLecture #BSMathematics #EngineeringStudents #CompetitiveExamPreparation #LearnWithArisha #NonlinearEquations #IterationMethod #MathematicsTutorial #MathConcepts #mathyoutube #SecantMethod #convergenceofsecantmethod #rateofconveregnceofsecantmethod #RegulaFalsi #FalsePositionMethod #NumericalMethods #NumericalAnalysis #GaussElimination #GaussJordan #NumericalMethods #LinearEquations #MatrixMethod #engineeringmathematics #PivotingStrategies #PartialPivoting #ScaledPartialPivoting #GaussElimination #NumericalMethods #NumericalAnalysis #LinearEquations #MatrixMethod #EngineeringMathematics #LearnWithArisha #LUDecomposition #DoolittleMethod #CroutMethod #NumericalMethods #linearalgebra #NumericalMethods #GaussSeidelMethod #JacobiMethod #IterativeMethods #SpecialMatrices #SparseMatrix #DenseMatrix #TridiagonalMatrix #BandMatrix #MatrixSparsity #PositiveDefiniteMatrix #DiagonallyDominantMatrix #LinearEquations #EngineeringMathematics #NumericalAnalysis #AppliedMathematics #ComputationalMathematics #ScientificComputing #MatrixMethods #LearnWithArisha