diff --git a/src/bokeh/palettes.py b/src/bokeh/palettes.py
index 2d899faaeb5..cdc03f9c3d4 100644
--- a/src/bokeh/palettes.py
+++ b/src/bokeh/palettes.py
@@ -412,13 +412,6 @@
 
 import logging # isort:skip
 log = logging.getLogger(__name__)
-
-#-----------------------------------------------------------------------------
-# Imports
-#-----------------------------------------------------------------------------
-
-# Standard library imports
-import math
 from copy import deepcopy
 from typing import TYPE_CHECKING, TypeAlias
 
@@ -1526,7 +1519,12 @@ def linear_palette(palette: Palette, n: int) -> Palette:
     """
     if n > len(palette):
         raise ValueError(f"Requested {n} colors, function can only return colors up to the base palette's length ({len(palette)})")
-    return tuple( palette[math.floor(i)] for i in np.linspace(0, len(palette)-1, num=n) )
+    # Optimization: avoid calling math.floor() for every index and iterating Python generator,
+    # use NumPy to get all integer indices in a vectorized manner, and use tuple comprehension.
+    indices = np.linspace(0, len(palette) - 1, num=n)
+    # Use np.floor/astype outside the generator to make indexing fast and avoid repeated math.floor calls
+    idx = indices.astype(int)
+    return tuple(palette[i] for i in idx)
 
 def diverging_palette(palette1: Palette, palette2: Palette, n: int, midpoint: float = 0.5) -> Palette:
     """ Generate a new palette by combining exactly two input palettes.