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A theory of natural observation methods was originally formulated for two-complementary systems; neighboring type and equilibrium type. This paper introduces a new system, normal-type system, that is different from the forementioned two types. One characteristics feature of the normal-type natural observation method is its ability to reconstruct an original waveform from the sum of a finite number of observation values. The natural observation theory of a normal type evolves naturally under the condition that waveform and its power component can be expressed in the sum form. These meanings are discussed by comparing a frequency response of the normal-type natural observation transform with that of a conventional filter bank. Furthermore, a criterion for determining observation parameters I order to realize the natural observation of normal type under a given tolerance of error is described. It is believed that the proposed theory offers new insights into systematization of the natural observation theory. [ABSTRACT FROM AUTHOR]

This paper discusses the eigenvalue problem for the real symmetric matrix, especially the determination of the largest eigenvalue. The largest eigenvalue is the maximum extremum of the objective function called the Rayleigh quotient and can be determined by the steepest descent method. It is known, however, that the steepest descent method suffers from slow convergence because it converges linearly. Especially, when the largest and the nest largest eigenvalues have very close values, the convergence is particularly slow. This paper analyzes this situation and shows that the convergence can be accelerated by combining the steepest descent method with a technique called shaking. Finally, it is demonstrated by a numerical example that the convergence is accelerated drastically by the proposed technique. [ABSTRACT FROM AUTHOR]

During the past few years, there been a series of paper published on the theory of the natural observation method. As one of the important application of this theory, the problems of acceptance and generation of a general waveform are discusses here. The case of polynomial waveforms and its corresponding theory was published previously. A great extension of the theory which general waveforms is presented here and its full picture is clarified. [ABSTRACT FROM AUTHOR]

Advances made in electronic computers allows the limit value of the sequence to be determined much more easily now than in the past. However, a problem still arises frequently in which it is difficult to determine the limit value with a high accuracy when a tremendous calculation is required in the determination of each term of the sequence. This paper proposes a theoretical method to estimate the limit value of the sequence with a high accuracy from the viewpoint of the recognition theory. By examining the gradual change of the sequence, the character inherent to the sequence is derived. By utilizing the character, the limit value can be estimated with a high accuracy directly from a small number of terms of the sequence. Lastly, the effectiveness of the proposed estimation method is demonstrated by simple examples. [ABSTRACT FROM AUTHOR]

A previous paper presented a method of transforming observed images from figure to 2nd-order differential figure. In this paper, the invariance of the figure source equation for observational transformation is discussed, when the theory is formed with the figure source equation as its core. The redefined observational transformation is constructed using three types of mapping: intensive transformation, blur transformation, and isomorphic transformation. The sets of these transformations form groups, and by making use of algebraic properties, it is possible to categorize the images. Furthermore, it is shown that the commutative law for transformational groups can be derived by analyzing their structure. © 1997 Scripta Technica, Inc. Syst Comm Jpn, 28(8): 44–53, 1997 [ABSTRACT FROM AUTHOR]

Theoretical studies on Iijima's “Theory of Pattern Recognition,” which is known as a method of multiple similarity, have shown dearly that there are situations when it is difficult to determine the viewpoint and visual field, important parameters to introduce topological aspects into the pattern space, observing a figure itself. To cope with this problem, this paper proposes transforming the observed image from a figure f(r) to a second-order differential image p(r), called “figure source.” The aim is to reconstruct the theory in such a way as to enable the application of similarity evaluation methods as in the conventional case, without compromising the current theory, and all the necessary proofs are given, In this paper, the figure source equation as well as rules representing its properties are developed, and several related physical quantities arc redefined. [ABSTRACT FROM AUTHOR]