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Shapiro, 1964 - Google Patents

Some negative theorems of approximation theory.

Shapiro, 1964

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Document ID
11986897855454613651
Author
Shapiro H
Publication year
Publication venue
Michigan Mathematical Journal

External Links

Snippet

Recently there has been some interest in so-called “negative theorems” of approximation theory, or more precisely, in lower bounds for the degree of approximation possible to functions of a given class by means of prescribed approximating functions. The main …
Continue reading at projecteuclid.org (PDF) (other versions)

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/22—Arrangements for performing computing operations, e.g. operational amplifiers for evaluating trigonometric functions; for conversion of co-ordinates; for computations involving vector quantities
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/26—Arbitrary function generators
    • G06G7/28—Arbitrary function generators for synthesising functions by piece-wise approximation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/20—Arrangements for performing computing operations, e.g. operational amplifiers for evaluating powers, roots, polynomes, mean square values, standard deviation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/16—Arrangements for performing computing operations, e.g. operational amplifiers for multiplication or division
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/14—Arrangements for performing computing operations, e.g. operational amplifiers for addition or subtraction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/4806—Computations with complex numbers
    • G06F7/4818—Computations with complex numbers using coordinate rotation digital computer [CORDIC]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/19—Arrangements for performing computing operations, e.g. operational amplifiers for forming integrals of products, e.g. Fourier integrals, Laplace integrals, correlation integrals; for analysis or synthesis of functions using orthogonal functions
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/48—Analogue computers for specific processes, systems or devices, e.g. simulators
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

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