Chapter 12' Introduction to Numerical Methods

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Chapter 12. Introduction to Numerical Methods

• Gauss-Jordan elimination method for solving
  system of linear equations
• portable random number generator

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• 12.1 Errors in numerical computations
• errors intrinsic to the nature of computers
• errors caused by inappropriate models
• Intrinsic errors
• caused by finite precision and range of computers
• Single-precision real number 32 bits
• 24 bits mantissa 6 or 7 significant digits
• 8 bits exponent 10-38 1038
• Double-precision real number 64 bits
• 53 bits mantissa 14 or 15 significant digits
• 11 bits exponent 10-308 10308

12345678.9 will be round-off to 12345680.0 for 7
significant digits ie. round-off error 1.1
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• 1.2.3 Type of data stored in memory
• The "real" or "floating point" data type in a
  type of scientific notation of base 2 system
  (value mantissa 2 exponent)
• For a real number occupy 32 bits of memory
• 24 bits for mantissa
• 8 bits for exponent
• a 24 bits mantissa can represent approximately
  223 8388608, ie. about 7 significatant digits
• a 8 bits exponent can represent approximately
  2-128 2127, ie. about 10-38 1038 range
• Ex. pi.f90

mmmmmmmmmmmmmmmmmmmmmmmmeeeeeeee
mantissa, precision
exponent, range