Are series representations of functions every practically used to graph in computer science?
As you probably know functions can be represented as a infinite series. For example f(x) = cosx can be represented as this. My question is if this is every used practically in programming for any type of application. I know it can be used I was just wondering if it actually is for serious projects.
math computer-science
asked Nov 19 '18 at 18:14
John ShoemakerJohn Shoemaker
83
add a comment |
As you probably know functions can be represented as a infinite series. For example f(x) = cosx can be represented as this. My question is if this is every used practically in programming for any type of application. I know it can be used I was just wondering if it actually is for serious projects.
math computer-science
asked Nov 19 '18 at 18:14
John ShoemakerJohn Shoemaker
83
I would say that discrete Fourier transforms are some of the most important representations of functions in computer science. Taylor series expansions of functions can have convergence issues. They aren't used for trig functions for efficiency reasons. But that doesn't mean they aren't useful.
– duffymo
Nov 19 '18 at 19:28
add a comment |
As you probably know functions can be represented as a infinite series. For example f(x) = cosx can be represented as this. My question is if this is every used practically in programming for any type of application. I know it can be used I was just wondering if it actually is for serious projects.
math computer-science
asked Nov 19 '18 at 18:14
John ShoemakerJohn Shoemaker
83
As you probably know functions can be represented as a infinite series. For example f(x) = cosx can be represented as this. My question is if this is every used practically in programming for any type of application. I know it can be used I was just wondering if it actually is for serious projects.
math computer-science
math computer-science
asked Nov 19 '18 at 18:14
John ShoemakerJohn Shoemaker
83
asked Nov 19 '18 at 18:14
John ShoemakerJohn Shoemaker
83
asked Nov 19 '18 at 18:14
John ShoemakerJohn Shoemaker
83
asked Nov 19 '18 at 18:14
John ShoemakerJohn Shoemaker
83
asked Nov 19 '18 at 18:14
John ShoemakerJohn Shoemaker
83
83
I would say that discrete Fourier transforms are some of the most important representations of functions in computer science. Taylor series expansions of functions can have convergence issues. They aren't used for trig functions for efficiency reasons. But that doesn't mean they aren't useful.
– duffymo
Nov 19 '18 at 19:28
add a comment |
I would say that discrete Fourier transforms are some of the most important representations of functions in computer science. Taylor series expansions of functions can have convergence issues. They aren't used for trig functions for efficiency reasons. But that doesn't mean they aren't useful.
– duffymo
Nov 19 '18 at 19:28
I would say that discrete Fourier transforms are some of the most important representations of functions in computer science. Taylor series expansions of functions can have convergence issues. They aren't used for trig functions for efficiency reasons. But that doesn't mean they aren't useful.
– duffymo
Nov 19 '18 at 19:28
I would say that discrete Fourier transforms are some of the most important representations of functions in computer science. Taylor series expansions of functions can have convergence issues. They aren't used for trig functions for efficiency reasons. But that doesn't mean they aren't useful.
– duffymo
Nov 19 '18 at 19:28
add a comment |
1 Answer
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Aside from infinite series, there are other representations for functions which can be useful for computing approximations. Asymptotic series, identities involving other "elementary" functions, and interpolation in a table of values are all used in different contexts. Take a look at Abramowitz & Stegun "Handbook of Mathematical Functions" to get an idea of the variety of possibilities. Also look for the source code for popular libraries or systems such as R, Numpy, Scipy, or Octave to see what approaches have been used by the authors of that software.
Specifically about series approximations for trigonometric functions, I think that might be a reasonable thing to do, but only if the range of the argument is reduced (via identities) so that it is as small as possible.
Approximation of functions is a great topic; good luck and have fun.
answered Nov 19 '18 at 20:39
Robert DodierRobert Dodier
11.1k11633
Citation of A&S is spot on.
– duffymo
Nov 20 '18 at 14:03
Very cool, thank you
– John Shoemaker
Nov 20 '18 at 21:46
add a comment |
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1 Answer
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1 Answer
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active
oldest
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votes
Aside from infinite series, there are other representations for functions which can be useful for computing approximations. Asymptotic series, identities involving other "elementary" functions, and interpolation in a table of values are all used in different contexts. Take a look at Abramowitz & Stegun "Handbook of Mathematical Functions" to get an idea of the variety of possibilities. Also look for the source code for popular libraries or systems such as R, Numpy, Scipy, or Octave to see what approaches have been used by the authors of that software.
Specifically about series approximations for trigonometric functions, I think that might be a reasonable thing to do, but only if the range of the argument is reduced (via identities) so that it is as small as possible.
Approximation of functions is a great topic; good luck and have fun.
answered Nov 19 '18 at 20:39
Robert DodierRobert Dodier
11.1k11633
Citation of A&S is spot on.
– duffymo
Nov 20 '18 at 14:03
Very cool, thank you
– John Shoemaker
Nov 20 '18 at 21:46
add a comment |
Aside from infinite series, there are other representations for functions which can be useful for computing approximations. Asymptotic series, identities involving other "elementary" functions, and interpolation in a table of values are all used in different contexts. Take a look at Abramowitz & Stegun "Handbook of Mathematical Functions" to get an idea of the variety of possibilities. Also look for the source code for popular libraries or systems such as R, Numpy, Scipy, or Octave to see what approaches have been used by the authors of that software.
Specifically about series approximations for trigonometric functions, I think that might be a reasonable thing to do, but only if the range of the argument is reduced (via identities) so that it is as small as possible.
Approximation of functions is a great topic; good luck and have fun.
answered Nov 19 '18 at 20:39
Robert DodierRobert Dodier
11.1k11633
Citation of A&S is spot on.
– duffymo
Nov 20 '18 at 14:03
Very cool, thank you
– John Shoemaker
Nov 20 '18 at 21:46
add a comment |
Aside from infinite series, there are other representations for functions which can be useful for computing approximations. Asymptotic series, identities involving other "elementary" functions, and interpolation in a table of values are all used in different contexts. Take a look at Abramowitz & Stegun "Handbook of Mathematical Functions" to get an idea of the variety of possibilities. Also look for the source code for popular libraries or systems such as R, Numpy, Scipy, or Octave to see what approaches have been used by the authors of that software.
Specifically about series approximations for trigonometric functions, I think that might be a reasonable thing to do, but only if the range of the argument is reduced (via identities) so that it is as small as possible.
Approximation of functions is a great topic; good luck and have fun.
answered Nov 19 '18 at 20:39
Robert DodierRobert Dodier
11.1k11633
Aside from infinite series, there are other representations for functions which can be useful for computing approximations. Asymptotic series, identities involving other "elementary" functions, and interpolation in a table of values are all used in different contexts. Take a look at Abramowitz & Stegun "Handbook of Mathematical Functions" to get an idea of the variety of possibilities. Also look for the source code for popular libraries or systems such as R, Numpy, Scipy, or Octave to see what approaches have been used by the authors of that software.
Specifically about series approximations for trigonometric functions, I think that might be a reasonable thing to do, but only if the range of the argument is reduced (via identities) so that it is as small as possible.
Approximation of functions is a great topic; good luck and have fun.
answered Nov 19 '18 at 20:39
Robert DodierRobert Dodier
11.1k11633
answered Nov 19 '18 at 20:39
Robert DodierRobert Dodier
11.1k11633
answered Nov 19 '18 at 20:39
Robert DodierRobert Dodier
11.1k11633
answered Nov 19 '18 at 20:39
Robert DodierRobert Dodier
11.1k11633
11.1k11633
Citation of A&S is spot on.
– duffymo
Nov 20 '18 at 14:03
Very cool, thank you
– John Shoemaker
Nov 20 '18 at 21:46
add a comment |
Citation of A&S is spot on.
– duffymo
Nov 20 '18 at 14:03
Very cool, thank you
– John Shoemaker
Nov 20 '18 at 21:46
Citation of A&S is spot on.
– duffymo
Nov 20 '18 at 14:03
Citation of A&S is spot on.
– duffymo
Nov 20 '18 at 14:03
Very cool, thank you
– John Shoemaker
Nov 20 '18 at 21:46
Very cool, thank you
– John Shoemaker
Nov 20 '18 at 21:46
add a comment |
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I would say that discrete Fourier transforms are some of the most important representations of functions in computer science. Taylor series expansions of functions can have convergence issues. They aren't used for trig functions for efficiency reasons. But that doesn't mean they aren't useful.
– duffymo
Nov 19 '18 at 19:28