New Optimization Algorithms to Calculate Roots of Polynomials

08092018, 03:05 AM
Post: #9




RE: New Optimization Algorithms to Calculate Roots of Polynomials
(08092018 01:37 AM)Claudio L. Wrote: I came across this page in Wikipedia: I used a good number of classical optimization algorithms with the Quasi LinBarstow 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^6x^5+2*x^44*x^38*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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