Results 1 
5 of
5
Constructive Analysis with Witnesses
"... Contents 1. Real Numbers 3 2 3 1.2. Reals, Equality of Reals 5 1.3. The Archimedian Axiom 6 1.4. Nonnegative and Positive Reals 6 1.5. Arithmetical Functions 7 1.6. Comparison of Reals 8 1.7. NonCountability 10 1.8. Cleaning of Reals 11 2. Sequences and Series of Real Numbers 11 2.1. Completenes ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Contents 1. Real Numbers 3 2 3 1.2. Reals, Equality of Reals 5 1.3. The Archimedian Axiom 6 1.4. Nonnegative and Positive Reals 6 1.5. Arithmetical Functions 7 1.6. Comparison of Reals 8 1.7. NonCountability 10 1.8. Cleaning of Reals 11 2. Sequences and Series of Real Numbers 11 2.1. Completeness 11 2.2. Limits and Inequalities 13 2.3. Series 13 2.4. Redundant Dyadic Representation of Reals 14 2.5. Convergence Tests 15 2.6. Reordering Theorem 17 2.7. The Exponential Series 18 3. The Exponential Function for Complex Numbers 21 4. Continuous Functions 23 4.1. Suprema and In ma 24 4.2. Continuous Functions 25 4.3. Application of a Continuous Function to a Real 27 4.4. Continuous Functions and Limits 28 4.5. Composition of Continuous Functions 28 4.6. Properties of Continuous Functions 29 4.7. Intermediate Value Theorem 30 4.8. Continuity of Functions with More Than One Variable 32 5. Dierentiation 33 5.1. Derivatives 33 5.2. Bounds on the Slope 33 5.3. Properties of Derivatives 34 5
Complexity and Intensionality in a Type1 Framework for Computable Analysis
 Computer Science Logic: 19th International Workshop, CSL 2005, 14th Annual Conference of the EACSL
"... Abstract. Implementations of real number computations have largely been unusable in practice because of their very bad performance, especially in comparison to floating point arithmetic implemented in hardware. This performance problem is to a very large extent due to the type2 nature of the comput ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Implementations of real number computations have largely been unusable in practice because of their very bad performance, especially in comparison to floating point arithmetic implemented in hardware. This performance problem is to a very large extent due to the type2 nature of the computable analysis frameworks usually employed. This problem can be overcome by employing a type1 approach. This paper presents such an approach and deals with properties of it that have not been well studied before, namely the introduction of complexity measures for type1 representations of real functions and ways to define intensional functions, i.e. functions that may return different real numbers for the same real argument given in different representations. 1