From 61b567ec19db87ec2ea1d61c56055c1e05f82ae7 Mon Sep 17 00:00:00 2001 From: Omur Ugur Date: Wed, 17 Sep 2025 13:11:55 +0300 Subject: [PATCH 1/3] broken links corrected --- tutorials/README.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/tutorials/README.md b/tutorials/README.md index 5851478..0d0a050 100644 --- a/tutorials/README.md +++ b/tutorials/README.md @@ -4,7 +4,7 @@ This package comes with a set of Jupyter notebooks designed as a structured tuto ## Core Tutorials -1. [Tutorial 1: Vectors and Matrices](tutorial1_vectors.ipynb) +1. [Tutorial 1: Vectors and Matrices](./tutorial1_vectors_matrices.ipynb) - Definitions of vectors and matrices. - Vector operations: addition, scalar multiplication, dot product, norms. @@ -12,7 +12,7 @@ This package comes with a set of Jupyter notebooks designed as a structured tuto - Matrix and vector norms. - Examples with `numethods.linalg`. -2. [Tutorial 2: Linear Systems of Equations](tutorial2_linear_systems.ipynb) +2. [Tutorial 2: Linear Systems of Equations](./tutorial2_linear_systems.ipynb) - Gaussian elimination and Gauss–Jordan. - LU decomposition. @@ -20,7 +20,7 @@ This package comes with a set of Jupyter notebooks designed as a structured tuto - Iterative methods: Jacobi and Gauss-Seidel. - Examples with `numethods.solvers`. -3. [Tutorial 3: Orthogonalization and QR Factorization](tutorial3_orthogonalization.ipynb) +3. [Tutorial 3: Orthogonalization and QR Factorization](./tutorial3_orthogonalization.ipynb) - Inner products and orthogonality. - Gram–Schmidt process (classical and modified). @@ -28,7 +28,7 @@ This package comes with a set of Jupyter notebooks designed as a structured tuto - QR decomposition and applications. - Examples with `numethods.orthogonal`. -4. [Tutorial 4: Root-Finding Methods](tutorial4_root_finding.ipynb) +4. [Tutorial 4: Root-Finding Methods](./tutorial4_root_finding.ipynb) - Bisection method. - Fixed-point iteration. From 094778f67e6ffaecc09eed213079e915e49191b9 Mon Sep 17 00:00:00 2001 From: Omur Ugur Date: Wed, 17 Sep 2025 13:28:33 +0300 Subject: [PATCH 2/3] more typo --- tutorials/tutorial2_linear_systems.ipynb | 2 +- tutorials/tutorial3_orthogonalization.ipynb | 12 ++++++------ tutorials/tutorial4_root_finding.ipynb | 2 +- 3 files changed, 8 insertions(+), 8 deletions(-) diff --git a/tutorials/tutorial2_linear_systems.ipynb b/tutorials/tutorial2_linear_systems.ipynb index 5cc6b7b..f0bceb0 100644 --- a/tutorials/tutorial2_linear_systems.ipynb +++ b/tutorials/tutorial2_linear_systems.ipynb @@ -15,7 +15,7 @@ "## Motivation\n", "Why we care about solving Ax=b? in numerical methods (e.g., arises in ODEs, PDEs, optimization, physics).\n", "\n", - "Exact solution: $ x=A^{-1}b $, but computing $ A^{-1} $ explicitly is costly/unstable.\n", + "Exact solution: $x = A^{-1}b$, but computing $A^{-1}$ explicitly is costly/unstable.\n", "\n", "Numerical algorithms instead use factorizations or iterative schemes.\n", "\n", diff --git a/tutorials/tutorial3_orthogonalization.ipynb b/tutorials/tutorial3_orthogonalization.ipynb index 38a8a4b..42d0426 100644 --- a/tutorials/tutorial3_orthogonalization.ipynb +++ b/tutorials/tutorial3_orthogonalization.ipynb @@ -94,7 +94,7 @@ "q_1 = \\frac{a_1}{\\|a_1\\|}\n", "$$\n", "$$\n", - "q_k = \\frac{a_k - \\sum_{j=1}^{k-1} (q_j \\cdot a_k) q_j}{\\left\\|a_k - \\sum_{j=1}^{k-1} (q_j \\cdot a_k) q_j\\right\\|}\n", + "q_k = \\frac{a_k - \\sum_{j=1}^{k-1} (q_j \\cdot a_k) q_j}{\\left\\|a_k - \\sum_{j=1}^{k-1} (q_j \\cdot a_k) q_j\\right\\|}, \\qquad k = 2, \\ldots, n\n", "$$\n", "\n", "Matrix form:\n", @@ -236,17 +236,17 @@ "\n", "We want to solve\n", "\n", - "$$ \\min_x \\|Ax - b\\|_2. $$\n", + "$$ \\min_x \\Vert Ax - b \\Vert_2^2. $$\n", "\n", "If $A = QR$, then\n", "\n", - "$$ \\min_x \\|Ax - b\\|_2 = \\min_x \\|QRx - b\\|_2. $$\n", + "$$ \\min_x \\Vert Ax - b \\Vert_2^2 = \\min_x \\Vert QRx - b \\Vert_2^2. $$\n", "\n", - "Since $Q$ has orthonormal columns:\n", + "Since $Q$ has orthonormal columns, and the normal equations boils down to\n", "\n", - "$$ R x = Q^T b. $$\n", + "$$ R x = Q^T b, $$\n", "\n", - "So we can solve using back-substitution.\n" + "we can therefore solve for $x$ by using back-substitution.\n" ] }, { diff --git a/tutorials/tutorial4_root_finding.ipynb b/tutorials/tutorial4_root_finding.ipynb index e6b2270..af8f759 100644 --- a/tutorials/tutorial4_root_finding.ipynb +++ b/tutorials/tutorial4_root_finding.ipynb @@ -55,7 +55,7 @@ "source": [ "## 2. Bisection Method\n", "\n", - "**Assumption (Intermediate Value Theorem):** If f is continuous on ([a,b]) and (f(a),f(b) < 0),\n", + "**Assumption (Intermediate Value Theorem):** If f is continuous on $[a,b]$ and $f(a),f(b) < 0$,\n", "then there exists $x^\\star$ in (a,b) with $f(x^\\star)=0$.\n", "\n", "- Assumes $f$ is continuous on $[a,b]$ with $f(a)f(b)<0$.\n", From 9fe1855fc6db7e960565f37c5ec6890f51982462 Mon Sep 17 00:00:00 2001 From: Omur Ugur Date: Wed, 17 Sep 2025 13:30:00 +0300 Subject: [PATCH 3/3] typo --- tutorials/tutorial4_root_finding.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tutorials/tutorial4_root_finding.ipynb b/tutorials/tutorial4_root_finding.ipynb index af8f759..0421535 100644 --- a/tutorials/tutorial4_root_finding.ipynb +++ b/tutorials/tutorial4_root_finding.ipynb @@ -55,7 +55,7 @@ "source": [ "## 2. Bisection Method\n", "\n", - "**Assumption (Intermediate Value Theorem):** If f is continuous on $[a,b]$ and $f(a),f(b) < 0$,\n", + "**Assumption (Intermediate Value Theorem):** If f is continuous on $[a,b]$ and $f(a)f(b) < 0$,\n", "then there exists $x^\\star$ in (a,b) with $f(x^\\star)=0$.\n", "\n", "- Assumes $f$ is continuous on $[a,b]$ with $f(a)f(b)<0$.\n",