Laguerre Methods

This project uses various Laguerre methods to solve polynomials.

Научный руководитель: Парфенов Денис Васильевич ([email protected])

КМБО-03-20: Александр Шашков ([email protected]), Вячеслав Иванов ([email protected]), Глеб Дорошенко ([email protected]), Дмитрий Балашов ([email protected]), Роман Охотников ([email protected]), Шахин Гаджиев ([email protected])

Documentation

MakeFile Variables

• SOLVER: The solver to use. Default is 2. Options are:

  • 0: Original Laguerre implementation
  • 1: On a family of Laguerre methods to find multiple roots of nonlinear equations
  • 2: An effective implementation of a modified Laguerre method for the roots of a polynomial

• NUMBER: The number type to use. Default is double.

• EXPONENT and MANTISSA: Used for root generator. Default values are 4 and 32 respectively.

• DEGREE: The degree of the polynomials. Default is 100.

• N_TESTS: The number of tests to run. Default is 10000.

• N_PAIRS_OF_COMPLEX_ROOTS, N_CLUSTERED_ROOTS, N_MULTIPLE_ROOTS: Parameters for the generator. If all are zero, then the generator will create only simple roots. Default values are 0, 0, and 0 respectively.

• MAX_DISTANCE_BETWEEN_CLUSTERED: Used only for clustered roots. Default is 1e-5.

• ROOT_SWEEP_LOW and ROOT_SWEEP_HIGH: The range for the root sweep. Default values are -1.0 and 1.0 respectively.

• TRIES: The number of iterations Laguerre should try to solve the polynomial. Default is 80.

Usage

To compile the program, run make.

To clean up the compiled files, run make clean.

For example, to run modified version of Laguerre with float type for polynomials degree of 5: make SOLVER=2 NUMBER=float DEGREE=5

We dont recommend to use float type for polynomial generation with degree higher than 5 - resulting coefficients will loose huge amount of precision during convertation from bignum to float. Double fails to work on degree greater than or equal to 200.