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Basic Routines

• Machine Epsilon - maceps

Error Routines

• Absolute Error - absolute_error
• Relative Error - relative_error
• Absolute Vector Error - absolute_error
• Relative Vector Error - relative_error

Root Finding

• Quadratic Equation - quadratic_equation
• Fixed Point Iteration - root_finder_fixed_point_iteration
• Bisection Method - root_finder_bisection
• Newton’s Method - root_finder_newton
• Secant Method - root_finder_secant
• Hybrid Newton’s Method - root_finder_hybrid_newton
• Hybrid Secant Method - root_finder_secant_method

Derivative Approximation

• Definition of the Derivative - deriv_approx

Norms

• l_p Vector Norms - l_pNorm
• l Infinity Vector Norm - l_inf
• One Matrix Norm - one_norm
• Infinity Matrix Norm - inf_norm
• Frobenius Matrix Norm - frobenius_norm

Vector Operations

• Vector Addition and Subtraction - Addition / Subtraction
• Vector Scalar Multiplication - Vector Scalar Multiplication
• Inner Product inner_product
• Cross Product cross_product
• Outer Product outer_product
• Orthogonal Basis orthogonal_basis

Matrix Operations

• Matrix Addition and Subtraction - Addition / Subtraction
• Transpose - Matrix Transpose
• Trace - Matrix Trace
• Scalar Matrix Multiplication - Scalar Matrix Multiplication
• Matrix Vector Multiplication - Matrix Vector Multiplication
• Matrix Matrix Multiplication - Matrix Matrix Multiplication
• Kronecker Product - kronecker_product
• Matrix Determinant - determinant
• Matrix Outer Product - a. Matrix Outer Product

Generators

• Matrix Generatorgenerate_square_symmetric_diagonally_dominant_matrix
• Right Side Generatorgenerate_right_side

Linear Solvers

• Solve By Gaussian Elimination - solve_linear_system_gaussian_elimination
  • Gaussian Elimination - gaussian_elimination
  • Back Substitution - back_substitution
• Solve By LU Factorization solve_linear_system_lu
  • LU Factorization - LU_factorization
  • Forward Substitution - forward_substitution
  • Back Substitution - back_substitution
• Solve By System Cholesky Factorization - solve_linear_system_cholesky
  • Cholesky Factorization - cholesky_factorization
• Jacobi Iteration - jacobi_iteration
• Gauss Seidel - gauss_seidel
• Conjugate Gradient / Steepest Descent - conjugate_gradient
• Parallel Jacobi Iteration - parallel_jacobi_iteration
• Parallel Gauss Seidel - parallel_gauss_seidel
• Parallel Conjugate Gradient - parallel_conjugate_gradient

Eigenvalue Methods

• Power Method - power_method
• Inverse Power Method - inverse_power_iteration
• 2 Condition Number Estimate - condition_2_estimate
• Parallel Power Method - parallel_power_iteration
• Parallel Inverse Power Method - parallel_inverse_power_iteration