Opposite of polyval
in [Matlab]
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From: Michael on 30 Mar 2010 11:58 Usually one calculates a polynomial using "polyfit" and then evaluates the polynomial at a certain position x using "polyval". How do I do it the other way round? If I have the polynomial coefficients and a certain value but want to know the position x? From a mathematical point of view, I would say there might be ambiguous solutions, which certainly will be a problem. But is there any function pre-implemented in MATLAB?
From: Bruno Luong on 30 Mar 2010 12:10 "Michael " <michael.schmittNOSPAM(a)bv.tum.de> wrote in message <hot72c$19d$1(a)fred.mathworks.com>... > Usually one calculates a polynomial using "polyfit" and then evaluates the polynomial at a certain position x using "polyval". > > How do I do it the other way round? If I have the polynomial coefficients and a certain value but want to know the position x? > > From a mathematical point of view, I would say there might be ambiguous solutions, which certainly will be a problem. But is there any function pre-implemented in MATLAB? help ROOTS Bruno
From: James Allison on 30 Mar 2010 12:42 roots will only provide the zeros of a polynomial, not x for a given y=f(x). fzero can do this, but is a more general method that does not take advantage of your function being a polynomial. As you mentioned, there may be multiple solutions to y=f(x) for a polynomial; fzero will find a solution that is near the starting point you specify. Here is an example: % create a polynommial y1 = [-1 8 17 19 10 -2 -7 -1 7 9]; x1 = 1:10; p = polyfit(x1,y1,5); % find values of x where polyval(p,x) = 5 y = 5; x0 = 1; f = @(x) polyval(p,x) - y; x = fzero(f,x0) % try with other starting points: x0 = 2; x = fzero(f,x0) x0 = 5; x = fzero(f,x0) x0 = 8; x = fzero(f,x0) The results are: x = 0.3507 x = 1.7616 x = 5.4230 x = 8.7112 which each correspond to a point where the polynomial is equal to y=5. -James Michael wrote: > Usually one calculates a polynomial using "polyfit" and then evaluates > the polynomial at a certain position x using "polyval". > > How do I do it the other way round? If I have the polynomial > coefficients and a certain value but want to know the position x? > > From a mathematical point of view, I would say there might be ambiguous > solutions, which certainly will be a problem. But is there any function > pre-implemented in MATLAB?
From: Walter Roberson on 30 Mar 2010 12:55 James Allison wrote: > roots will only provide the zeros of a polynomial, not x for a given > y=f(x). Since it is a polynomial, you can roots() of f(x)-y
From: Bruno Luong on 30 Mar 2010 12:57
James Allison <james.allison(a)mathworks.com> wrote in message <hot9lg$d67$1(a)fred.mathworks.com>... > roots will only provide the zeros of a polynomial, not x for a given > y=f(x). P(x) = f(x)-y is polynomial, and what is the root of P(x)? Bruno |