Newton-Raphson 迭代求根计算器

POST http://127.0.0.1:3003/zh/api/tools/newton-raphson-root-finder

{
  "mcpServers": {
    "elysiatools-newton-raphson-root-finder": {
      "name": "newton-raphson-root-finder",
      "description": "用 Newton-Raphson 迭代 x_{k+1} = x_k − f(x_k)/f'(x_k) 求 f(x) = 0 的根：导数可给定解析表达式（留空则用中心差分数值导数），输出逐步迭代表（x_k 与 f(x_k)）、收敛判据（|f| < 容差或 |Δx| < 容差·max(1,|x|)）、迭代次数与最终 |f(root)|。经典例：x²−2 从 x₀=1 出发 4 步收敛到 √2 ≈ 1.4142135624；cos(x)−x 收敛到 Dottie 数 0.7390851332。导数为零、步长发散或超出迭代上限会明确报告。",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=newton-raphson-root-finder",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "newton-raphson-root-finder",
    "arguments": {
  "fxExpr": "x^2 - 2",
  "dfxExpr": "",
  "x0": 1,
  "tolerance": 1e-10,
  "maxIter": 50,
  "decimalPlaces": 10
}
  }
}