meaning that the diagonal matrix is a numerical approximation to the spectrum of the differential operators. Matrix diagonalization has a high computational cost [2]. Symmetric Tridiagonal Eigenvalue Solvers pose significant computational challenges, including the renowned divide-and-conquer algorithm (also known as [PERSON]'s algorithm [3]). To address [PERSON]'s algorithm, parallel computing techniques have been employed to enhance their efficiency [4], often leveraging heterogeneous parallel architectures involving both CPUs and GPUs. However, it is essential to note that GPUs have limited memory capacity compared to CPUs, imposing constraints on the size of the problems that can be effectively tackled. Two popular libraries, LAPACK [5] and MAGMA [6], have emerged as notable solutions for eigenvalue problem-solving. LAPACK, also known as the Linear Algebra PACKage, is a sequential library that is the foundation for other linear algebra libraries. It is extensively utilized in many applications that rely on linear algebra operations. Additionally, there exist optimized versions of LAPACK, with Intel MKL [7] being renowned for its exceptional performance. This implementation can be executed either sequentially or in parallel using multicore processors. Conversely, MAGMA represents the successor to LAPACK and is explicitly designed to harness the power of multicore processors and graphics processing units (GPUs) through its Matrix Algebra on GPU and Multicore Architectures. However, it should be noted that MAGMA does not take advantage of multiple nodes [8], which restricts the size of matrices that can be effectively solved, particularly for routines utilizing a single GPU. Using a divide-and-conquer implementation across multiple nodes has the potential to alleviate this restriction. Substantial improvements in execution time can be achieved by employing parallel programming techniques on heterogeneous architectures. Additionally, taking advantage of GPUs' low energy consumption, as highlighted in studies by [9; 10] can further reduce costs while maximizing resource utilization. In this work, we propose implementing the divide-and-conquer algorithm for symmetric tridiagonal matrix diagonalization. We aim to combine this algorithm with a heterogeneous hybrid parallel approach, utilizing GPUs and CPUs across multiple nodes. The objective is to evaluate the suitability of this approach in terms of accuracy and execution time. Through this investigation, we seek to gain insights into the performance and effectiveness of this methodology. To parallelize the algorithm, we employ GPUs with the Nvidia CUDA platform (NvidiaCUDA 5.5) (NVIDIA, Santa Clara, CA, USA), Intel multi-core processors utilizing OpenMP (with gcc 4.7.3), and multiple nodes through message transmission using MPI (OpenMPI 1.7.1), as depicted in Figure 1. Our experimental tests demonstrate that the solutions obtained from the heterogeneous parallel implementation exhibit high accuracy, as evidenced by the orthogonality of eigenvectors and the quality of eigenpairs. The main contributions of this work include introducing a scalable hybrid-heterogeneous parallel implementation (GPUs + CPUs) of the divide-and-conquer algorithm for symmetric tridiagonal matrix diagonalization across multiple nodes. To the best of our knowledge, this is the first implementation of its kind. Our research has led to a significant reduction in the computational time of symmetric tridiagonal matrix diagonalization, surpassing the performance of state-of-the-art libraries in parallel and sequential versions. We slightly modify the algorithm to enhance performance even in a sequential version. One of our notable achievements is the increased independence from the amount of GPU memory in the implementation, a significant step towards more efficient and flexible computing. We are enhancing scalability in the implementation, facilitating the handling of larger data sets.