New Optimization Algorithms to Calculate Roots of Polynomials
08-09-2018, 03:05 AM
Post: #9
 Namir Senior Member Posts: 823 Joined: Dec 2013
RE: New Optimization Algorithms to Calculate Roots of Polynomials
(08-09-2018 01:37 AM)Claudio L. Wrote:  I came across this page in Wikipedia:

https://en.wikipedia.org/wiki/Test_funct...timization

It has a lot of functions to test optimization methods. Some are trickier than others. I thought it might be of interest to anyone trying optimization methods.

I used a good number of classical optimization algorithms with the Quasi Lin-Barstow algorithm to factor out quadratic equations from the targeted polynomial. Of course there is virtually an infinite number of polynomials to test. As the order of the polynomial increases so does the combination of polynomial coefficients. I came across several cases where where the optimization algorithms gave wrong answers!! The cases that I saw had the coefficients (as the power of each term) increase half way and then drop (something like x^10 + 2*x^9 -4*x^8+12*x^7+18*x^6-x^5+2*x^4-4*x^3-8*x^2+9*x+10 = 0).

I am assuming there must be a polynomial property that determines how easy it is to solve for its roots. Such a property would be equivalent to the condition number of a matrix that determines how easy it is to solve a system of linear equations

Namir
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 Messages In This Thread New Optimization Algorithms to Calculate Roots of Polynomials - Namir - 08-06-2018, 01:35 PM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Luigi Vampa - 08-07-2018, 08:53 AM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Namir - 08-07-2018, 09:56 PM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Claudio L. - 08-08-2018, 02:26 AM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Namir - 08-08-2018, 03:30 AM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Albert Chan - 08-08-2018, 12:06 PM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Namir - 08-08-2018, 03:34 PM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Claudio L. - 08-09-2018, 01:37 AM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Namir - 08-09-2018 03:05 AM RE: New Optimization Algorithms to Calculate Roots of Polynomials - ttw - 08-09-2018, 03:57 AM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Thomas Klemm - 08-09-2018, 11:30 AM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Namir - 08-09-2018, 11:51 AM RE: New Optimization Algorithms to Calculate Roots of Polynomials - Namir - 08-10-2018, 02:38 AM

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