I am modelling physical system with heat conduction, and to do numerical calculations I need to solve system of linear equations with tridiagonal matrix. I am using this algorithm to get results: http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm But I am afraid that my method is straightforward and not optimal. What C++ library should be used to solve that system in the fastest way? I should also mention that matrix is not changed often (only right part of the equation is changed). Thanks!
Library for solving system of linear equations with tridiagonal matrix?
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The performance of this algorithm is likely dominated by floating-point division. Use SSE2 to perform two divisions (of ci and di) at once, and you will get close to optimal performance.
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It is worth looking at the LAPACK and BLAS interfaces, of which there are several implementation libraries. Originally netlib which is open-source, and then other such as MKL that you have to pay for. The function dgtsv does what you are looking for. The open-source netlib versions don't do any explicit SIMD instructions, but MKL does and will perform best on intel chips.
Check out Eigen.