main: some modification and typos #4
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.gitignore
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.gitignore
vendored
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PhiloMath
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data-fitting-models
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data-fitting-models
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/
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.gitignore
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Ömür Uğur
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f9860d7f48
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Initial commit
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2 days ago
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357 lines
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6.4 KiB
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Plaintext
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# ---> JupyterNotebooks
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# gitignore template for Jupyter Notebooks
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# website: http://jupyter.org/
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48
README.md
48
README.md
@@ -10,55 +10,9 @@ A lightweight, from-scratch, object-oriented Python package implementing classic
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- Lightweight, no dependencies.
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- Consistent object-oriented API (.solve() etc).
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---
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## Tutorial Series
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This package comes with a set of Jupyter notebooks designed as a structured tutorial series in **numerical methods**, both mathematically rigorous and hands-on with code.
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### Core Tutorials
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1. [Tutorial 1: Vectors and Matrices](tutorials/tutorial1_vectors.ipynb)
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- Definitions of vectors and matrices.
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- Vector operations: addition, scalar multiplication, dot product, norms.
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- Matrix operations: addition, multiplication, transpose, inverse.
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- Matrix and vector norms.
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- Examples with `numethods.linalg`.
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2. [Tutorial 2: Linear Systems of Equations](tutorials/tutorial2_linear_systems.ipynb)
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- Gaussian elimination and Gauss–Jordan.
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- LU decomposition.
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- Cholesky decomposition.
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- Iterative methods: Jacobi and Gauss-Seidel.
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- Examples with `numethods.solvers`.
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3. [Tutorial 3: Orthogonalization and QR Factorization](tutorials/tutorial3_orthogonalization.ipynb)
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- Inner products and orthogonality.
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- Gram–Schmidt process (classical and modified).
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- Householder reflections.
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- QR decomposition and applications.
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- Examples with `numethods.orthogonal`.
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4. [Tutorial 4: Root-Finding Methods](tutorials/tutorial4_root_finding.ipynb)
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- Bisection method.
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- Fixed-point iteration.
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- Newton’s method.
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- Secant method.
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- Convergence analysis and error behavior.
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- Trace outputs for iteration history.
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- Examples with `numethods.roots`.
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- [Polynomial Regression Demo](tutorials/polynomial_regression.ipynb)
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- Step-by-step example of polynomial regression.
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- Shows how to fit polynomials of different degrees to data.
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- Visualizes fitted curves against the original data.
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---
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This package comes with a set of Jupyter notebooks designed as a structured tutorial series in **numerical methods**, both mathematically rigorous and hands-on with code. See [Tutorials](./tutorials/README.md).
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## Features
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47
tutorials/README.md
Normal file
47
tutorials/README.md
Normal file
@@ -0,0 +1,47 @@
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# Tutorial Series
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This package comes with a set of Jupyter notebooks designed as a structured tutorial series in **numerical methods**, both mathematically rigorous and hands-on with code.
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## Core Tutorials
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1. [Tutorial 1: Vectors and Matrices](./tutorial1_vectors.ipynb)
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- Definitions of vectors and matrices.
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- Vector operations: addition, scalar multiplication, dot product, norms.
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- Matrix operations: addition, multiplication, transpose, inverse.
|
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- Matrix and vector norms.
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- Examples with `numethods.linalg`.
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2. [Tutorial 2: Linear Systems of Equations](./tutorial2_linear_systems.ipynb)
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- Gaussian elimination and Gauss–Jordan.
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- LU decomposition.
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- Cholesky decomposition.
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- Iterative methods: Jacobi and Gauss-Seidel.
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- Examples with `numethods.solvers`.
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3. [Tutorial 3: Orthogonalization and QR Factorization](./tutorial3_orthogonalization.ipynb)
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- Inner products and orthogonality.
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- Gram–Schmidt process (classical and modified).
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- Householder reflections.
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- QR decomposition and applications.
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- Examples with `numethods.orthogonal`.
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4. [Tutorial 4: Root-Finding Methods](./tutorial4_root_finding.ipynb)
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- Bisection method.
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- Fixed-point iteration.
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- Newton’s method.
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- Secant method.
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- Convergence analysis and error behavior.
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- Trace outputs for iteration history.
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- Examples with `numethods.roots`.
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- [Polynomial Regression Demo](./polynomial_regression.ipynb)
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- Step-by-step example of polynomial regression.
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- Shows how to fit polynomials of different degrees to data.
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- Visualizes fitted curves against the original data.
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---
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@@ -142,7 +142,7 @@
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"## 5. Basic operations\n",
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"\n",
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"### 5.1 Vector addition and subtraction\n",
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"For $ u, v \\in \\mathbb{R}^n $:\n",
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"For $u, v \\in \\mathbb{R}^n$:\n",
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"\n",
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"$$\n",
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"u + v = \\begin{bmatrix} u_1 + v_1 \\\\ u_2 + v_2 \\\\ \\vdots \\\\ u_n + v_n \\end{bmatrix},\n",
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@@ -180,7 +180,7 @@
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"metadata": {},
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"source": [
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"### 5.2 Scalar multiplication\n",
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"For $ \\alpha \\in \\mathbb{R}, v \\in \\mathbb{R}^n $:\n",
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"For $\\alpha \\in \\mathbb{R}, v \\in \\mathbb{R}^n$:\n",
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"\n",
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"$$\n",
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"\\alpha v = \\begin{bmatrix} \\alpha v_1 \\\\ \\alpha v_2 \\\\ \\vdots \\\\ \\alpha v_n \\end{bmatrix}.\n",
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@@ -215,7 +215,7 @@
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"metadata": {},
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"source": [
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"### 5.3 Matrix addition and subtraction\n",
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"For $ A, B \\in \\mathbb{R}^{m \\times n} $:\n",
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"For $A, B \\in \\mathbb{R}^{m \\times n}$:\n",
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"\n",
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"$$\n",
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"A + B = [ a_{ij} + b_{ij} ], \\quad\n",
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@@ -254,7 +254,7 @@
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"metadata": {},
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"source": [
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"### 5.4 Matrix-Vector multiplication\n",
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"For $ A \\in \\mathbb{R}^{m \\times n}, v \\in \\mathbb{R}^n $:\n",
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"For $A \\in \\mathbb{R}^{m \\times n}, v \\in \\mathbb{R}^n$:\n",
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"\n",
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"$$\n",
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"(Av)_i = \\sum_{j=1}^n a_{ij} v_j.\n",
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@@ -290,7 +290,7 @@
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"metadata": {},
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"source": [
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"### 5.5 Matrix-Matrix multiplication\n",
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"For $ A \\in \\mathbb{R}^{m \\times n}, B \\in \\mathbb{R}^{n \\times p} $:\n",
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"For $A \\in \\mathbb{R}^{m \\times n}, B \\in \\mathbb{R}^{n \\times p}$:\n",
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"\n",
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"$$\n",
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"(AB)_{ij} = \\sum_{k=1}^n a_{ik} b_{kj}.\n",
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@@ -327,7 +327,7 @@
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"metadata": {},
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"source": [
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"### 5.6 Transpose\n",
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"For $ A \\in \\mathbb{R}^{m \\times n} $:\n",
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"For $A \\in \\mathbb{R}^{m \\times n}$:\n",
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"\n",
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"$$\n",
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"A^T_{ij} = A_{ji}.\n",
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