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14 Linear Algebra

This chapter describes functions for solving linear systems. The library provides linear algebra operations which operate directly on the gsl_vector and gsl_matrix objects. These routines use the standard algorithms from Golub & Van Loan’s Matrix Computations with Level-1 and Level-2 BLAS calls for efficiency.

The functions described in this chapter are declared in the header file gsl_linalg.h.

• LU Decomposition:  
• QR Decomposition:  
• QR Decomposition with Column Pivoting:  
• Complete Orthogonal Decomposition:  
• Singular Value Decomposition:  
• Cholesky Decomposition:  
• Pivoted Cholesky Decomposition:  
• Modified Cholesky Decomposition:  
• Tridiagonal Decomposition of Real Symmetric Matrices:  
• Tridiagonal Decomposition of Hermitian Matrices:  
• Hessenberg Decomposition of Real Matrices:  
• Hessenberg-Triangular Decomposition of Real Matrices:  
• Bidiagonalization:  
• Givens Rotations:  
• Householder Transformations:  
• Householder solver for linear systems:  
• Tridiagonal Systems:  
• Triangular Systems:  
• Balancing:  
• Linear Algebra Examples:  
• Linear Algebra References and Further Reading:  

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