Aritmetički i algebarski algoritmi -- seminarske teme


Zadnja promjena: 30.03.2008. u 14:20.


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Popis tema (u nekim blokovima)


Jednostavni algoritmi:

  1. A New Algorithm for Inner Product (Daniela Trečić)

Pretvaranje iz baze u bazu:

  1. High-Speed Binary-to-Decimal Conversion (Petra Dunkel)

Verižni razlomci:

  1. Application of Continued Fractions for Fast Evaluation of Certain Functions on a Digital Computer (Filip Nikšić)
  2. On the Use of Continued Fractions for Digital Computer Arithmetic (Perica Levatić)
  3. A Method for Solving Polynomial Equations by Continued Fractions (Lucija Vojnović)

Dijeljenje:

  1. Generation of Products and Quotients Using Approximate Binary Logarithms for Digital Filtering Applications (pdf, 1777 kB)
  2. An Augmented Iterative Array for High-Speed Binary Division (Marko Ilić)
  3. Integer Division Using Reciprocals (Zoran Pucarin)
  4. On-Line Algorithms for Division and Multiplication (Mladen Zmazek)
  5. The Correspondence Between Methods of Digital Division and Multiplier Recoding Procedures (pdf, 1888 kB)
  6. On Division by Functional Iteration (Tomislav Poparić)
  7. Higher-Radix Division Using Estimates of the Divisor and Partial Remainders (pdf, 1704 kB)
  8. A Polynomial-Based Division Algorithm (Semir Ajruli)

Dijeljenje (nastavak):

  1. Multiprecision Integer Division Examples Using Arbitrary Radix (Marija Borovac)
  2. An Overrelaxation for a Numerical Inverse of a Constant (pdf, 710 kB)
  3. Speeding up an Overrelaxation Method of Division in Radix-2^n Machine (pdf, 496 kB)

Dijeljenje (još malo):

  1. On Range-Transformation Techniques for Division (pdf, 921 kB)
  2. On Optimal Iterative Schemes for High-Speed Division (pdf, 832 kB)
  3. A Division Algorithm for Signed-Digit Arithmetic (Ankica Barišić)

Euklidov algoritam:

  1. Analysis of fast versions of the Euclid Algorithm (Marko Haberl)

Brza Fourierova transformacija:

  1. Fast Computational Algorithms for Bit Reversal (pdf, 3227 kB)
  2. A Generalization of the Fast Fourier Transform (Jelena Špekuljak)
  3. A New Hybrid Algorithm for Computing a Fast Discrete Fourier Transform (Marin Vila)
  4. Fourier Transform Computers Using CORDIC Iterations (pdf, 2838 kB)
  5. An Algorithm for the Machine Computation of Partial-Fractions Expansion of Functions Having Multiple Poles (pdf, 806 kB)

Elementarne funkcije u floating-pointu:

  1. Parallel Multiplicative Algorithms for Some Elementary Functions (pdf, 766 kB)
  2. More Efficient Radix-2 Algorithms for Some Elementary Functions (Ante Ćustić)
  3. High-Speed Double-Precision Computation of Reciprocal, Division, Square Root, and Inverse Square Root (pdf, 731 kB)
  4. Economic Pseudodivision Processes for Obtaining Square Root, Logarithm, and Arctan (pdf, 784 kB)
  5. A Digit-by-Digit Algorithm for m-th Root Extraction (Ines Šimičić)

Euklidska norma vektora u floating-pointu:

  1. Programming Pearls - Birth of a Cruncher (Euclidean distance) (Hrvoje Rožaj)
  2. A Portable Fortran Program To Find the Euclidean Norm of a Vector (Krešimir Bokulić)

Zaokruživanje u floating-pointu:

  1. A Comparison of Three Rounding Algorithms for IEEE Floating-Point Multiplication (Filip Radovčić)
  2. Analysis of Rounding Methods in Floating-Point Arithmetic (Vlado Udić)

Množenje:

  1. Uniform Shift Multiplication Algorithms Without Overflow (Toni Petrina)
  2. The Quasi-Serial Multiplier (Josip Deak)
  3. A Binary Multiplication Scheme Based on Squaring (Nives Fakin)
  4. High-Speed Computer Multiplication Using a Multiple-Bit Decoding Algorithm (pdf, 627 kB)
  5. On Binary Multiplication Using the Quarter Square Algorithm (Ive Grbić)
  6. A Proof of the Modified Booth's Algorithm for Multiplication (Frano Topić)
  7. An Efficient Polynomial-Modulus Based Technique for Multiplication of Large Integers (Maja Novaković)

Negativne baze:

  1. Arithmetic Algorithms in a Negative Base (Iva Barišić)
  2. Deterministic Division Algorithm in a Negative Base (pdf, 1794 kB)
  3. Complementary Two-Way Algorithms for Negative Radix Conversions (pdf, 1205 kB)
  4. Divide-and-Correct Algorithm for Division in a Negative Base (Josip Paić)
  5. Arithmetic Algorithms in a Negative Base (Filip Crljenić)

Složenost operacija:

  1. Hardware Complexity of Modular Multiplication and Exponentiation (Danijela Perić)

Numeričke aproksimacije funkcija:

  1. Optimal Piecewise Polynomial L_2 Approximation of Functions of One and Two Variables (Ksenija Kitanov)
  2. A Piecewise Linear Approximation of log_2 x with Equal Maximum Errors in All Intervals (Goran Kreminski)

Generiranje pseudoslučajnih brojeva:

  1. A More Portable Fortran Random Number Generator (Ivo Špelić)

Aritmetika u sustavima ostataka:

  1. Sign Detection in Residue Number Systems (Mia Sanader)

Simetrični sustavi ostataka:

  1. Floating-Point Arithmetic Algorithms in the Symmetric Residue Number System (pdf, 3668 kB)
  2. General Division in the Symmetric Residue Number System (pdf, 3406 kB)

Nije primjereno, ali ako netko baš želi:

  1. On the Parallel Evaluation of Polynomials (pdf, 715 kB)
  2. The Relationship Between Two Fast Fourier Transforms (pdf, 1760 kB)
  3. Mathematical Foundation of Computer Arithmetic (pdf, 3225 kB)
  4. Floating-Point Computation of Functions with Maximum Accuracy (pdf, 3721 kB)
  5. A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital Computer (pdf, 3325 kB)
  6. A Formalization of Floating-Point Numeric Base Conversion (pdf, 2867 kB)
  7. Properties of the Multidimensional Generalized Discrete Fourier Transform (pdf, 3088 kB)
  8. Implementation of FFT Structures Using the Residue Number System (pdf, 4820 kB)
  9. Using an Efficient Sparse Minor Expansion Algorithm to Compute Polynomial Subresultants and the Greatest Common Denominator (pdf, 1732 kB)
  10. Numerical Technique for the Convolution of Piecewise Polynomial Functions (pdf, 3042 kB)
  11. An Algorithm for Redundant Binary Bit-Pipelined Rational Arithmetic (pdf, 1088 kB)