add and fix some

notes/1.ipynb

@@ -18,7 +18,9 @@
    "source": [
     "# Floating Point\n",
     "\n",
-    "**Double Precision Floating Point Number Representation**\n",
+    "$$s\\times M \\times B^{e-E}$$\n",
+    "\n",
+    "**IEEE-754 Double Precision Floating Point Number Representation**\n",
     "\n",
     "$$(-1)^s \\times 2^{c-1023} \\times (1+f)$$\n",
     "\n",
@@ -31,13 +33,35 @@
    "cell_type": "markdown",
    "id": "9c0b5413",
    "metadata": {},
-   "source": []
+   "source": [
+    "## Machine Accuracy\n",
+    "\n",
+    "$$\\epsilon = b^{1-m}$$\n",
+    "\n",
+    "(typically $b = 2$, $m: \\text {bit for matissa}$)\n"
+   ]
   },
   {
    "cell_type": "markdown",
    "id": "964d247f",
    "metadata": {},
-   "source": []
+   "source": [
+    "# Errors\n",
+    "\n",
+    "* **Round-off Error**\n",
+    "\n",
+    "* **Truncation Error**\n",
+    "\n",
+    "Taylor Series\n",
+    "\n",
+    "approximations: zero order, first order(recommended), second order, etc..\n",
+    "\n",
+    "let $v_t$: true value, and $v_a$: approximation\n",
+    "Absolute error: $(v_t - v_a)$\n",
+    "Relative error: $(v_t - v_a) / v_t$\n",
+    "\n",
+    "so stopping condition is $e_a < e_s$ where $e_s$ is desired.\n"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -48,8 +72,7 @@
     "\n",
     "When there is no or hard to find analytic solution.\n",
     "\n",
-    "* General procedure of root finding\n",
-    "\n",
+    "General procedure of root finding\n",
     "\n",
     "## Incremental Search\n",
     "\n",