Solvers for linear systems of equations with symmetric positive-definite matrices are required for many applications such as structural analysis with the finite element method, electromagnetic transients simulations or System Identification with Gaussian Processes. Since very large systems can emerge when dealing with such applications the solving process can become computationally very demanding. For this reason, GPUs are often used to speed up the computation. However, current computer systems are often still equipped with powerful CPUs. Thus, homogeneous approaches that only leverage the GPU do not fully utilize the theoretical capabilities of the whole system. Heterogeneous computing addresses this issue as it aims to use the CPU and GPU of a system simultaneously to achieve an even better performance. In this work heterogeneous implementations of two solvers, the conjugate gradient (CG) method and the Cholesky decomposition, are developed and applied to Gaussian Processes for behavior prediction of a mass-spring-damper system. The heterogeneous algorithms are implemented using SYCL, which allows to target CPUs and GPUs from different vendors while only relying on standard C++ as a programming language. The heterogeneous implementations of both algorithms will be compared to classical homogeneous approaches on the CPU and GPU in terms of performance and energy efficiency on various hardware. The results show that the heterogeneous implementations are able to achieve significant performance improvements over the homogeneous implementations. For a matrix with 65536 times 65536 entries, the heterogeneous CG method achieves up to 32 percent faster results than the GPU-only implementation and the heterogeneous Cholesky decomposition is up to 29 percent faster in a similar scenario. Furthermore, for large matrices, the heterogeneous Cholesky decomposition is able to achieve at least twelve percent faster runtimes than the GPU-only version across multiple systems with various GPUs from NVIDIA, AMD and Intel, all with the same SYCL code.