{
  "id": "lib-process:mathematics--numerical-stability-analysis",
  "_kind": "LibraryProcess",
  "_file": "generated-library/processes.yaml",
  "_cluster": "generated-library",
  "attributes": {
    "displayName": "numerical-stability-analysis",
    "description": "Analyze numerical algorithms for stability, convergence, and error propagation.\nIncludes condition number analysis, floating-point error bounds, and stability assessment for various input ranges.",
    "libraryPath": "library/specializations/domains/science/mathematics/numerical-stability-analysis.js",
    "specialization": "mathematics",
    "references": [
      "- Higham, Accuracy and Stability of Numerical Algorithms\n- Golub & Van Loan, Matrix Computations\n- IEEE 754 Floating-Point Standard\n- Trefethen & Bau, Numerical Linear Algebra"
    ],
    "example": "const result = await orchestrate('specializations/domains/science/mathematics/numerical-stability-analysis', {\n  algorithm: 'Gaussian elimination with partial pivoting',\n  algorithmCode: 'def gaussian_elimination(A, b): ...',\n  inputDomain: { matrixSize: [2, 1000], conditionRange: [1, 1e6] },\n  precisionRequirements: { relativeTolerance: 1e-10, absoluteTolerance: 1e-15 }\n});",
    "usesAgents": [
      "numerical-analyst"
    ]
  },
  "outgoingEdges": [
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "skill-area:statistical-analysis",
      "kind": "lib_requires_skill_area",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "skill-area:mathematical-reasoning",
      "kind": "lib_requires_skill_area",
      "attributes": {
        "weight": 0.7
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "skill-area:data-analysis",
      "kind": "lib_requires_skill_area",
      "attributes": {
        "weight": 0.5
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "domain:mathematics",
      "kind": "lib_applies_to_domain",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "role:research-engineer",
      "kind": "lib_involves_role",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "role:computational-scientist",
      "kind": "lib_involves_role",
      "attributes": {
        "weight": 0.7
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "workflow:experiment-design",
      "kind": "lib_implements_workflow",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "specialization:computational-mathematics",
      "kind": "lib_belongs_to_specialization",
      "attributes": {
        "weight": 1
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "specialization:mathematics",
      "kind": "lib_belongs_to_specialization",
      "attributes": {
        "weight": 0.9
      }
    },
    {
      "from": "lib-process:mathematics--numerical-stability-analysis",
      "to": "lib-agent:mathematics--numerical-analyst",
      "kind": "uses_agent",
      "attributes": {
        "weight": 0.8
      }
    }
  ],
  "incomingEdges": []
}