Term

Definition
A solution exists, is unique, and depends continuously on the problem data 


Term

Definition
In order to find an accurate solution, a problem must be wellposed and wellconditioned, and an algorithm must be stable. 


Term

Definition
The difference between exact function values due to error in input 


Term

Definition
Difference between exact and approximate function values for the same input. Composed of truncation and rounding error. 


Term

Definition
Difference between true result and that produced by a given algorithm using exact arithmetic. 


Term

Definition
Difference between the result produced by a given algorithm using exact arithmetic and result produced by same algorithm using finiteprecision. 


Term

Definition
Discrepency between computed and true values:
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Term

Definition
The quantity [image] where [image] 


Term
Conditioning of a problem 

Definition
Effects of propagated data error on the solution of a problem
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Term
Stability of an algorithm 

Definition
The effects of computational error on the result computed by an algorithm 


Term

Definition
Expressed as a number of moderate size times a power of ten. Base (usually two), Precision(53), Lower exponent (1022) and upper exponent (1023). 


Term

Definition
Round to zero (chop): fl(x) is truncated after the (p1)st digit, where p is precision
Round to nearest: fl(x) is the nearest floatingpoint number to x 


Term

Definition
Bounds the relative error in representing any nonzero real number x within the normalized range of a floatingpoint system
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Term
Floatingpoint arithmetic 

Definition
Adding/Subtracting: Exponents must match, so shifted first. Trailing digits of smaller number are lost.
Multiplication: exponents are summed and mantissas are multiplied. Two pdigit mantissas contains up to 2p digits. 


Term

Definition
Subtraction between two pdigit numbers having the same sign and similar magnitudes yields a result with fewer than p significant digits; exactly representable; potential serious loss of information 


Term

Definition
Describes limiting behavior of a function when the argument tends towards a particular value or infinity. 

