Generation of test matrices with specified eigenvalues using floating-point arithmetic

Uniform Random Generation of Decomposable Structures Using Floating-Point Arithmetic

The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to oating-point arithmetic. The resulting ADZ method enables one to generate decomposable data structures | both labelled or unlabelled | uniformly at random, in expected O(n ) time and space, after a preprocessing phase of O(n ) time, which reduces to O(n ) f...

Floating-Point Arithmetic

A Test of a Computer ’ s Floating - Point Arithmetic Unit

This paper describes a test of a computer's floating-point arithmetic unit. The test has two goals. The first goal deals with the needs of users of computers, and the second goal deals with manufacturers of computers. The first and major goal is to determine if the machine supports a particular mathematical model of computer arithmetic. This model was developed as an aid in the design, analysis...

Elements of Floating-point Arithmetic

Precision Arithmetic: A New Floating-Point Arithmetic

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid the excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding r...