Accelerated computational schemes for symbolic and numeric algorithms

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The objective of this research program is to develop a set of algorithms, software and hardware tools for acceleration of some standard symbolic and numeric algorithms. Our target symbolic algorithms are in the area of symbolic summation. The target numeric algorithms focus on high precision evaluation of elementary and special functions. Our approach to the acceleration is based on -- symbolic preprocessing of computational problems, including the choice of an appropriate representation, for example, closed form formula, annihilating linear differential or difference operator, chains of recurrences, integral representation of combinatorial sums and code generation based on chosen representation; -- use of alternative arithmetics for high precision computations such as modular representation of arbitrary precision rational numbers with special choice of moduli, adaptive precision floating-point arithmetic; -- distributing computationally hard problems over a network of workstations or through the web; -- VHDL prototyping of specialized hardware for acceleration of a particular computational task, including prototyping of specialized floating point units based on the technique of multidimensional chains of recurrences and adaptive precision floating-point arithmetic.