Solving quartic equations in Excel.

  • Thread starter Thread starter nikos
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nikos

Hi.
Does anyone written a method which solves quartic equations in an Excel
sheet ?
Th.
 
Hi.
Does anyone written a method which solves quartic equations in an Excel
sheet ?
Th.
Click to expand...

If you have only one equation to solve, then a simple method is to
rewrite the equation in the form y = f(x) = 0 then find the
approximate solutions by drawing a graph of y = f(x) and seeing
rough;y where it crosses the Y axis. Now find each solution more
exactly by using Solver.
 
Thank you but i was looking for an example written in an Excel sheet and not
a general describe about quartic models.
(I have written a simple method to solve the quartic equation in Excel but
in some cases does not give exact solutions and i was looking for something
similar to compare the formulas. Probably has to do with the accuracy of the
complex numbers that i use.)
 
nikos -

Quartic = polynomial of order 4

(1) I worked on quartic solutions with a math-PhD colleague several years
ago, and, as I recall, his method for a "closed-form" solution had several
cases and several sub-cases. I didn't ever implement his method using Excel
VBA, and I doubt that I could find the notes from that era. The specific
application where I wanted to use it had some special structure so that a
bisection search could be used efficiently (and if I ever continue to
research it further I might be able to speed up convergence using
Newton-Raphson search for portions of this specific problem).

(2) For a one-time solution of a quartic (as opposed to a solution function
that will be repeatedly recalculated with different parameters, i.e., with
different coefficients of the 4th-order polynomial), I would try to use a
search method like Goal Seek or Solver. Post again with your specific
parameters if you need help setting it up.

- Mike
http://www.MikeMiddleton.com


Hi.
Does anyone written a method which solves quartic equations in an Excel
sheet ?
Th.
 
Thank you but i was looking for an example written in an Excel sheet and not
a general describe about quartic models.
(I have written a simple method to solve the quartic equation in Excel but
in some cases does not give exact solutions and i was looking for something
similar to compare the formulas. Probably has to do with the accuracy of the
complex numbers that i use.)
Click to expand...

Does your reference to complex numbers mean that you are looking for
all solutions, real and complex?
 
It has been proved that there is no formula for quintic and upper degree
equations. Up to fourth degree polynomials has been extract analytical
solutions.
 
I just came across this thread.

The link below has a downloadable spreadsheet (including open source code) with UDFs that will do what you want:

http://newtonexcelbach.wordpress.com/2011/01/13/solving-higher-order-polynomials/

There are UDFs to solve up to quartic using analytical methods, and one using an iterative method that will solve "any" order polynomial. In all cases the UDF returns all the real and complex roots, the number of roots of each type, and an estimate of the maximum error.
Hi.
Does anyone written a method which solves quartic equations in an Excel
sheet ?
Th.
On Monday, February 01, 2010 1:53 AM Ro wrote:
The answer may be yes!
Look at this link:
http://www.ac.cc.md.us/Department/math.html/eisen2/ch2.htm

"nikos" wrote:
Click to expand...
//www.purplemath.com/modules/solvquad4.htm[/URL]
Click to expand...
Click to expand...
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