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Introductory to Numerical Analysis การวิเคราะห์เชิงตัวเลขเบื้องต้น 01417343. by Suriya Na nhongkai. ความคลาดเคลื่อนฝังติด (Inherent error) เกิดจากการที่เราไม่สามารถจำลองแบบของธรรมชาติได้ตามปรากฏการณ์ที่เกิดขึ้นจริง ความผิดพลาดจากการวัดข้อมูล ความคลาดเคลื่อนจากการปัดเศษ (Round-off error) - PowerPoint PPT Presentation
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Introductory to Numerical Analysis 01417343
Introductory to Numerical Analysis01417343by
Suriya Na nhongkaiType of Errors (Inherent error) (Round-off error) (Truncation error) (continuous system) (discrete system)Definition of Error
Error: Example
Accuracy Identification
General Rounding off n
General Rounding off 5000... n 5000... 5000... n General Rounding off: Example
Propagated Error
9Propagated Error: Addition and Subtraction
Propagated Error Addition and Subtraction: Example11Propagated Error: Multiplication
Propagated ErrorMultiplication: Example 1
Propagated ErrorMultiplication: Example 2Propagated Error: Division
Propagated ErrorDivision: Example
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus
Fundamental Theorem in Calculus: Example
Fundamental Theorem in Calculus: Taylors Theorem
Fundamental Theorem in Calculus: Taylors TheoremFundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Fundamental Theorem in Calculus Taylors Theorem: Example
Rounding off and Computer Arithmetic
Rounding off and Computer Arithmetic
Rounding off and Computer Arithmetic: Example 32 IBM 3000 IBM 4300 1 7 ( 16) 24
7 0 127 64 -64 63Rounding off and Computer Arithmetic: Example
Sign bit 0
Rounding off and Computer Arithmetic: Example
179.015625
Rounding off and Computer Arithmetic: IEEE-754 Single Precision
Rounding off and Computer Arithmetic: IEEE-754 Double PrecisionRounding off in Calculator
Chopping and Rounding
Rounding off in Calculator: ExampleRounding off in Calculator: Example
Rounding off in Calculator: Example
Rounding off in Calculator: Example
Rounding off in Calculator: Example
1
(Absolute error)
= 0.5225 =0.5237
= 0.5225-0.5237 = -0.0012
= = 0.0023 (Decimal Place, D.P.) x = 3.14725 3 D.P. x = 3.147 (Significant Digit, S.D.)
0.012041 0.31470 5 4 (Error Bound)
0.0012 123.456789012345623456
n 123.456789012345623000 5.4565725 2 D.P. 5.46 3 D.P. 5.457 6 D.P. 5.456572 5 S.D. 5.4566 n D.P. 3 S.D.
3 D.P. 8 D.P.
3 D.P. 2 D.P.
1 D.P. 2 D.P. 3 D.P.
0 D.P. -151
()
(2 D.P.) (3 D.P.) 1 D.P.
1. 2.
(Rolls Theorem)
(Mean Value Theorem)
Slope slope (Extreme Value Theory) , (Riemann Integral)
,
(Weighted Mean Value Theorem for Integral) ,
(Intermediate Value Theorem) . (Taylors Theorem)
(Taylor Polynomial) (Remainder Term or Truncation Error) () (Maclaurin Series) (1) (2)
0
8 D.P.
9 D.P. 0.99995000042 9(2)
0.099833417 6 D.P.
( )
,
0.04
3 (6 D.P.)
5 D.P.
5 D.P.
2
3
3
(Significant Number) (Mantissa) (Characteristic) () 123.4567 0.00021378
179.0156097412109375 179.0156402587890625Single Precision 32 1 () 8 () 23 ()
Double Precision 64-bit 1 () 11 () 52 ()
()
(Chopping) (Rounding)Chopping Rounding 1 33 Single Precision IEEE-754 33 24 Normalize1. 1 ( 1 )2. 0 ()
1 1
Sign (s)Characteristic (c)Mantissa (f)
+128
Single Precision IEEE-754 0.1
Normalize
Rounding
4 Sign (s)Characteristic (c)Mantissa (f)
+123