PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPROXIMATION THEORY NAAT2006, CLUJ-NAPOCA (ROMANIA), JULY 5–8, 2006, pp.1–12 EFFICIENT ALGORITHMS FOR HERMITE INTERPOLATION NICULESCU VIRGINIA (1) Abstract. This paper proposes a method for general (arbitrary or- der of the derivatives information) Hermite interpolation. Based on this method, sequential and parallel algorithms are analyzed. For the parallel algorithm we consider bounded parallelism, thus a practical approach. It means that we will consider the number of the processes p to be a parameter of the parallel programs derivation. The obtained algorithm uses set-distributions and is cost-efficient. 1. Introduction Lagrange and Hermite interpolations are well known methods of poly- nomial interpolation, and at the same time they are of great importance since they are widely used. Their parallelization has been discussed before, and parallel algorithms with good time complexities have been obtained [1, 5, 6, 3, 7, 15, 16]. But these parallel algorithms have been constructed considering only unbounded parallelism, which means that the number of processes that have to be used could become impractically large. For La- grange interpolation, very good complexities O(log n) have been obtained, provided that large number of processors are used - polynomial in the size of the problem (n) [1, 9]. If the number of processor was limited to n, and spe- cial interconnection networks used (star graph, k-ary cube, tree augmented with ring connections, systolic), then complexities equal to O(n) have been obtained [7, 15, 16]. Also, there is an algorithm with a complexity equal to O( √ n) using a multi-mesh of k 2 (k = n 2 ) processors presented by M. De [4]. For general Hermite interpolation, where the input is a set of dis- tinct points (m), and corresponding to each point, prescribed values for the function and all its derivatives up to some arbitrary order (r), Egecioglu et al. [5, 6] have described a parallel algorithm with a O(log 2 n + log r) complexity, provided that more than O(n 2 r) processors are used. 2000 Mathematics Subject Classification. code, code. Key words and phrases. interpolation, parallel computation. 1