שגיאת קיטום

באנליזה נומרית ובמדע חישובי, שגיאת קיטום היא השגיאה שנוצרת על ידי הגבלת אורכו של סכום אינסופי וקירובו בסכום סופי. למשל, אם מחשבים את ערכה של פונקציית הסינוס באמצעות שני האיברים הראשונים שאינם אפסים בסדרת טיילור שלה (למשל, עבור $x$ קטן, מחשבים $\sin(x)\approx x-{\tfrac {1}{6}}x^{3}$ ), השגיאה שמתקבלת היא שגיאת קיטום. הוא קיים אפילו עם חשבון דיוק אינסופי, מכיוון שהוא נגרם על ידי קטיעה של סדרת טיילור האינסופית ליצירת האלגוריתם.

לעיתים קרובות, שגיאה בקיצוץ כוללת גם שגיאת דיקרטיזציה, שהיא הטעות הנובעת מביצוע מספר סופי של צעדים בתוך חישוב המקרב תהליך אינסופי. לדוגמה, בשיטות נומריות לפתרון משוואות דיפרנציאליות רגילות, הפונקציה המשתנה ברציפות, שהיא הפתרון של המשוואה הדיפרנציאלית מקורבת על ידי תהליך שמתקדם שלב אחר שלב, והשגיאה הכרוכה בכך היא טעות דיסקרטיזציה או קטיעה.

לעיתים, שגיאת עיגול (התוצאה של שימוש בייצוג נקודה צפה סופי במחשבים) נקראת גם היא שגיאת קיטום, במיוחד אם המספר מעוגל באמצעות קיטום.

ראו גם

שגיאת קוונטיזציה

לקריאה נוספת

Atkinson, Kendall E. (1989), An Introduction to Numerical Analysis (2nd ed.), New York: John Wiley & Sons, p. 20, ISBN 978-0-471-50023-0
Stoer, Josef; Bulirsch, Roland (2002), Introduction to Numerical Analysis (3 ed.), Berlin, New York: Springer-Verlag, p. 1, ISBN 978-0-387-95452-3.

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