Berkeley COMPSCI 282 - Lecture Notes (24 pages)

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Lecture Notes



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Computer Algebra Systems Numerics Lecture 17 Richard Fateman CS 282 Lecture 17 1 Symbolic Computation includes numeric as a subset Why do CAS not entirely replace numeric programming environments Richard Fateman CS 282 Lecture 17 2 Symbolic Computation vs Purely Numeric Systems prosper Why loss in efficiency is not tolerated unless something sophisticated is going on the symbolic system adds more complexity than necessary learning curve CAS systems are extra cost Other reasons People are successful in the first approach they learned They don t change How else to explain Fortran Richard Fateman CS 282 Lecture 17 3 What is the added value for Symb Num SENAC like systems Computer Algebra front end help systems Code generation systems GENTRAN integrated visualization interaction plotting exact integer and rational arithmetic extra precision seamlessly interval arithmetic explicit endpoints range in Maple Interval in MMa implicit intervals significance arithmetic Richard Fateman CS 282 Lecture 17 4 Numerics tend to be misunderstood Insufficient explanation about what is going on Peculiar user expectations Is 3 000 more accurate than 3 0 Is it more precise Why is sum 0 001 i 1 1000 only 0 99994 Mathematica default makes simple convergent processes diverge Richard Fateman CS 282 Lecture 17 5 Square root of 9 by Newton Iteration s x x x2 9 2 x Nest s 2 5 11641532182693481445313 38805107275644938 15104 differs from 3 by 1 3880510727564493815104 Nest s 2 0 5 3 0 0 start interation at 2 Nest s 2 000000000000000 5 3 0 x10 18 Nest s 2 000000000000000 50 3 0 x10 5 r Nest s 2 000000000000000 70 3 0 Nest s 2 00000000000000000000000000 88 2 0 umh you mean the iteration also converges to 2 Richard Fateman CS 282 Lecture 17 6 It looks like it was getting worse and then got better InputForm r is 0 0 4771 furthermore r 1 prints as 0 Richard Fateman CS 282 Lecture 17 7 Mathematica has gotten more elaborate AccuracyGoal WorkingPrecision SetPrecision beyond simple characterization Claims v



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