README.md

SIAM Article Template for CoCalc

Professional SIAM-style article template optimized for CoCalc with integrated Python computational examples for numerical mathematics and scientific computing research.

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Features

• SIAM-Style Formatting: Single-column academic format with proper margins and typography

• PythonTeX Integration: Embedded Python code for numerical experiments and analysis

• Numerical Mathematics Focus: Iterative methods, convergence analysis, and matrix computations

• Reproducible Computations: All numerical results generated during compilation

• Theorem Environments: Comprehensive mathematical theorem, definition, and proof environments

• Professional Figures: Computational plots and convergence analysis generated programmatically

• SEO-Optimized: Comprehensive keywords and metadata for discoverability

Quick Start

Compilation in CoCalc

1. Standard Build (recommended):

   make
   

2. Using latexmk:

   latexmk -pdf main.tex
   

3. Manual compilation:

   pdflatex -shell-escape main.tex
   pythontex main.tex
   pdflatex -shell-escape main.tex
   pdflatex -shell-escape main.tex
   

Important Notes

• Shell Escape Required: This template requires -shell-escape flag for PythonTeX

• Python Dependencies: Uses numpy, matplotlib, scipy (pre-installed in CoCalc)

• Compilation Time: First build may take 60-90 seconds due to numerical computations

Template Structure

article-siam/
├── main.tex           # Main SIAM-style article document
├── Makefile          # Build automation
├── latexmkrc         # LaTeXmk configuration
├── README.md         # This documentation
└── [generated files] # Created during compilation
    ├── convergence_analysis.pdf
    ├── convergence_analysis.png
    └── pythontex-files-main/

Computational Features

Numerical Analysis Examples

The template includes working Python code that generates:

1. Iterative Method Comparison: Classical vs. accelerated conjugate gradient algorithms

2. Matrix Generation: Test matrices with controlled condition numbers and spectral properties

3. Convergence Analysis: Comprehensive convergence rate studies and statistical validation

4. Performance Metrics: Computational efficiency and iteration count comparisons

5. Spectral Analysis: Eigenvalue distribution and clustering effects

Key Mathematical Content

• Classical conjugate gradient (CG) algorithm implementation

• Adaptive accelerated CG with momentum optimization

• Theoretical convergence bounds and practical performance analysis

• Numerical linear algebra computational experiments

• Statistical validation across multiple test problems

CoCalc-Specific Features

TimeTravel Integration

Create checkpoints after successful builds:

1. Build the document: make

2. In CoCalc, go to TimeTravel tab

3. Create checkpoint: "SIAM template - numerical experiments complete"

Collaboration Features

• Real-time Editing: Multiple researchers can edit simultaneously

• Mathematical Discussion: Built-in chat for discussing numerical results

• Version Control: TimeTravel for tracking computational experiment changes

• AI Assistant: Use Claude for mathematical content enhancement

AI Integration Suggestions

Use CoCalc's AI assistant for:

• Algorithm Development: "Help me implement a preconditioned CG method"

• Mathematical Writing: "Improve the convergence theorem statement"

• Code Optimization: "Optimize this matrix generation code for large problems"

• Result Interpretation: "Analyze these convergence rate differences"

Customization

Adapting for Different SIAM Journals

1. SIAM Journal on Scientific Computing: Focus on computational algorithms

2. SIAM Review: Add more expository content and broader context

3. SIAM Journal on Matrix Analysis: Emphasize matrix-theoretic results

4. SIAM Journal on Optimization: Include optimization problem formulations

Mathematical Environment Usage

The template provides comprehensive theorem environments:

\begin{theorem}[Convergence Rate]
Your theorem statement here.
\end{theorem}

\begin{proof}
Your proof here.
\end{proof}

\begin{algorithm}[Adaptive CG]
\begin{algorithmic}[1]
\STATE Initialize variables
\FOR{each iteration}
    \STATE Update step
\ENDFOR
\end{algorithmic}
\end{algorithm}

Extending Numerical Examples

Add new computational sections by:

1. Creating new \begin{pycode} blocks

2. Implementing relevant numerical algorithms

3. Generating analysis plots and performance tables

4. Including convergence rate studies

Troubleshooting

Common Issues

Unicode Character Errors

• The template uses standard LaTeX math symbols instead of Unicode

• Greek letters should be written as $\kappa$ not κ

• Use $\lambda$ instead of λ in mathematical expressions

PythonTeX Compilation Issues

# Check PythonTeX availability
which pythontex
# Clean and rebuild if needed
make clean && make

Long Compilation Times

• Numerical experiments may take time on first build

• Use make draft for quick builds without Python execution

• PythonTeX caches results for faster subsequent builds

Mathematical Formatting

Equation Numbering

• Use \begin{equation} for numbered equations

• Use \begin{align} for multi-line equations

• Reference with \eqref{eq:label}

Algorithm Formatting

• Use the algorithmic environment for pseudocode

• Number algorithm lines with [1] option

• Include complexity analysis in algorithm descriptions

Performance Tips

1. Development Workflow: Use make draft during writing, make for final builds

2. Incremental Builds: PythonTeX caches computational results

3. File Management: Use make clean to remove auxiliary files

4. Large Computations: Consider breaking large experiments into smaller code blocks

Scientific Applications

This template is particularly well-suited for:

• Numerical Linear Algebra: Iterative solvers, matrix factorizations, eigenvalue problems

• Optimization: Gradient methods, constrained optimization, convex analysis

• Scientific Computing: Discretization methods, numerical PDEs, computational physics

• Applied Mathematics: Mathematical modeling, asymptotic analysis, perturbation theory

License

This template is provided under MIT License. Feel free to adapt for your research needs.

Contributing

Improvements and extensions welcome! Focus areas:

• Additional numerical algorithms (GMRES, BiCGSTAB, etc.)

• Optimization method implementations

• Finite element and finite difference examples

• Advanced mathematical environments

Citation

When using this template for SIAM journal submissions, ensure you:

1. Follow SIAM's specific formatting guidelines

2. Include proper AMS subject classifications

3. Use SIAM's preferred citation style

4. Acknowledge computational resources (CoCalc)

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Optimized for: SIAM journals, numerical analysis research, computational mathematics, scientific computing applications, CoCalc LaTeX environment