Sorry, no online dictionaries contain the exact phrase root-finding algorithms.
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Reverse dictionary results:
1. inverse quadratic interpolation
 2. methods of computing square roots
3. halley's method
4. root system
5. newton's method
6. newton's method in optimization
7. secant method
8. ridders' method
9. algorithm
10. muller's method
 11. algebraic number
12. laguerre's method
13. numerical method
14. divisor function
15. bisection method
16. root test
17. fixed-point iteration
18. householder's method
19. cycle detection
20. inverse iteration
 21. computational problem
22. riemann solver
23. biconjugate gradient method
24. index calculus algorithm
25. quadratic programming
26. computable number
27. conjugate gradient method
28. sliding dft
29. integer factorization records
30. operation
 31. special number field sieve
32. root cause analysis
33. midpoint method
34. analytic number theory
35. fixed-point combinator
36. gaussian elimination
37. optimization problem
38. broyden's method
39. stochastic approximation
40. prime-counting function

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