github.com/almostinf/computational_mathematics

computational_mathematics

Task 1

• direct problem of error theory
• Complete inverse problem of error theory

This is my variant: z(x) =√sin(x+ 0.74) sh(0.8x2+ 0.1), x= 0.1(0.01)0.2;

Task 2

• Implementation of LU decomposition of a matrix with selection of the leading element by column, also the check LU = PAQ is implemented Using the LU decomposition, we find:
  • matrix determinant
  • solution to SLAE Ax = b is found
  • inverse matrix
  • conditionality number
• modified algorithm for finding the rank of degenerate matrices
• QR decomposition
• Jacobi and Seidel methods for solving SLAEs. A priori and posterior estimates are implemented

Task 3

Implementation of Newton method and modified Newton method of scalar nonlinear algebraic equation and system of nonlinear algebraic equations

Task 4

• Newton-Cotes method implementation
• implementation of Gauss method
• error estimated by Richardson method
• the speed of convergence is estimated by the Aitken rule

This is my variant: f(x) = 3 cos(1.5x) exp(x/4) + 4 sin(3.5x) exp(-3x) + 4x, a= 2.5, b= 3.3, α=2/3, β= 0