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Numerical analysis

The numerical analysis falls into several subdivisions,  as follows
1-Introduction to numerical analysis.

2-Solving non-linear equations.

3-Solving Linear equations.

4-Interpolation.

10-Solved problems for 3×3 matrix by Crout’s LU-option 1.

September 18, 2025November 1, 2024 by Maged kamel
Two solved problems for The Crout's LU decomposition.

Two solved problems for 3×3 matrix by Crout’s LU decomposition. Option 1 is used for which the matrix is converted to a lower matrix.

Categories Solution of linear systems Tags solved problems for (3x3) matrix by Crout's LU decomposition.

9A- A Second option for Crout’s LU decomposition-3×3 matrix

September 18, 2025October 29, 2024 by Maged kamel
brief illustration post 9 numerical linear

A Second option for Crout’s LU decomposition-3×3 matrix. How to covert the A matrix to an upper matrix? How to get the values of L and U matrices?

Categories Solution of linear systems Tags Second option for Crout's LU decomposition for a 3x3 matrix

9- Crout’s LU decomposition for a 3×3 matrix-Option 1

September 18, 2025April 1, 2024 by Maged kamel
Crout's LU decomposition for a 3x3 matrix-Option 1

How to drive Crout’s LU decomposition for a 3×3 matrix-option-1? Step-by-step introduction to Crout’s LU decomposition for a 3×3 matrix.

Categories Solution of linear systems Tags Crout's LU decomposition for a 3x3 matrix-option 1

8-Introduction to Crout’s LU decomposition for a 2×2 matrix.

September 18, 2025March 5, 2024 by Maged kamel
brief description of post 8 content.

How to drive Crout’s LU decomposition for a 2×2 matrix? Step-by-step introduction to Crout’s LU decomposition with a solved problem.

Categories Solution of linear systems Tags Introduction to Crout's LU decomposition for a 2x2 matrix

7-A Solved problem 9-5 LU decomposition.

September 18, 2025February 25, 2024 by Maged kamel
A Solved problem 9-5 LU decomposition.

Solved problem 9-5 LU decomposition from reference book Numerical methods for engineers. We will verify our solution with the author’s solution.

Categories Solution of linear systems Tags Solved problem 9.5 Lu decomposition.

5c- Easy approach to permutation matrix-part 2.

September 18, 2025November 22, 2023 by Maged kamel
An easy approach to permutation matrix-part 2.

In the Permutation matrix-part 2, we continue the discussion about the various types of Permutation matrices.

Categories Solution of linear systems Tags Permutation matrix for a 3x3 matrix.

5b- Easy introduction to permutation matrix.

October 3, 2025November 22, 2023 by Maged kamel
An easy introduction to permutation matrix.

The post includes an introduction to the permutation matrix for both 2×2 and 3×3 matrices. How to change the arrangement of rows and columns for matrices?

Categories Solution of linear systems Tags Introduction to Permutation matrix.

2d-Solved problems for Newton-divided differences.

May 20, 2024October 9, 2021 by Maged kamel
brief illustration - post 2d-numerical-interpolation

Two Solved problems for Newton-divided differences are given for more information about the method.

Categories Introduction to Interpolation Tags Solved problems for Newton-divided differences.

2c- What is Newton-divided difference interpolation?

October 21, 2024October 6, 2021 by Maged kamel
brief illustration- post 2c-numerical-interpolation

Learn about deriving the expression of Newton-Divided difference interpolation function and how to derive the expression.

Categories Introduction to Interpolation Tags Introduction to Newton-divided difference interpolation.

2b- Solved problems for quadratic interpolation

May 19, 2024May 7, 2021 by Maged kamel
brief illustration - post 2b-numerical-interpolation

Solved problems for quadratic interpolation. In both two solved problems three points, are given and used to get the quadratic interpolation function.

Categories Introduction to Interpolation Tags Solved problems for quadratic interpolation.

2a- Easy introduction to quadratic interpolation.

July 13, 2025April 12, 2021 by Maged kamel
brief illustration - post 2a-numerical-interpolation

Quadratic interpolation, how to derive the expression of it? The Vandermonde matrix and how to get its inverse value and determinant value?

Categories Introduction to Interpolation Tags Quadratic interpolation, Vandermonde matrix

1- Easy introduction to the definition of Interpolation.

July 13, 2025April 8, 2021 by Maged kamel
brief illustration - post 1-numerical-interpolation

An introduction to interpolation and linear interpolation, what are polynomials, and how can be used as a tool to make a linear interpolation?

Categories Introduction to Interpolation Tags Interpolation, Linear Interpolation

5A- Second solved problem-LU decomposition-3×3 matrix.

September 22, 2025January 20, 2021 by Maged kamel
Second solved problem-LU decomposition-3×3 matrix.

The second solved problem-LU decomposition for the 3×3 matrices, how to get x,y,z values for three simultaneous equations?

Categories Solution of linear systems Tags A second Solved problem for LU for 3x3 matrix.

5- First solved problem-LU decomposition for the 3×3 matrix

October 7, 2025January 15, 2021 by Maged kamel
First solved problem-LU decomposition for the 3x3 matrix.

This post illustrates the first solved problem-LU decomposition for the 3×3 matrix. Step by step guide to solve 3 simultaneous equations by the LU method?

Categories Solution of linear systems Tags Solved problems for Lu decomposition for 3x3 matrix.

4-Derive the expression for L-U values for-3×3 matrix.

September 17, 2025December 1, 2020 by Maged kamel
Brief illustration of Post 4- numerical linear.

Step-by-step guide on how to derive the expression for L-U values for-3×3 matrix using Doolittle’s method?

Categories Solution of linear systems Tags How to derive the expression for L-U values for-3x3 matrix?
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