CN108563613A - A kind of Mathematical Modeling Methods using computer hyperspace - Google Patents
A kind of Mathematical Modeling Methods using computer hyperspace Download PDFInfo
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Abstract
The invention discloses a kind of Mathematical Modeling Methods using computer hyperspace, and in particular to mathematical modeling technology field.Which solve it is existing modeled using computer technology when, need to be related to largely to calculate and professional knowledge, operation and its cumbersome, it is difficult to the deficiency of grasp.Method specifically includes：By computer acquisition system gathered data and analyze discrete；Model hypothesis is carried out according to discrete data, space dimensionality is determined, each dimension data of hyperspace is respectively filled in determinant；Determinant is simplified by linear algebra theory, and establishes functional relation；Discrete data is brought into and carries out verification operation in function；If the error of verification is excessive, return to step four re-establishes functional relation；Reach stipulated number if retried, return redefines suitable space dimensionality；Simplify the mathematical relationship between each dimension, each dimension is made individually to linearize.
Description
Technical field
The present invention relates to mathematical modeling technology fields, and in particular to a kind of mathematical modeling side using computer hyperspace
Method.
Background technology
Since nearly over half a century, with the rapid development of computer technology, the application of mathematics not only engineering technology, from
The fields such as right science play increasingly important role, and with unprecedented breadth and depth to economic, management, finance, raw
The new field infiltration such as object, medicine, environment, geology, population, traffic, so-called mathematical technique have become contemporary new and high technology
Important component.
Mathematical modeling is exactly the result that is obtained by computer come solving practical problems, and receives the inspection of practical problem,
Carry out the overall process of founding mathematical models.When needing from one practical problem of quantitative angle analysis and research, people will be
On the basis of stretching into investigation, understanding object information, make the work such as simplified design and analysis inherent law, with the symbol of mathematics
Number and language make statement come founding mathematical models.Mathematical model is a kind of simulation, practical mathematic sign, mathematics formula, program, figure
The abstract youngster to actual subject essential attribute such as shape succinct quarter, it or can explain certain objective phenomenons, or can predict future
The rule of development, can in order to control a certain phenomenon development provide certain meaning under optimal policy or compared with good strategy.
Mathematical model is not generally the direct turnover panel of realistic problem, its foundation had usually both needed people to realistic problem depth
Enter subtle observation and analysis, and people is needed flexibly dexterously to utilize various mathematical knowledges.This working knowledge is from practical class
The process that mathematical model is abstracted, extracted in topic is known as mathematical modeling.
When applied mathematics goes to solve all kinds of practical problems, founding mathematical models are a very crucial steps, while being also ten
Divide a difficult step.The process for establishing teaching mode is that complicated practical problem is simplified, is abstracted as rational mathematics knot
The process of structure.Will by inquiry, collect data information, observation and research practical object inherent feature and inherent law, catch
The principal contradiction of problem, it is established that reflect the quantitative relation of practical problem, then using mathematics theory and method go analysis and
It solves the problems, such as.This just needs deep sturdy Fundamentals of Mathematics, sharp insight and imagination, to the great interest of practical problem
With extensive the scope of one's knowledge.Mathematical modeling is connection mathematics and the bridge of practical problem, is that mathematics is widely applied in every field
Medium, is the main path of science of mathematics technical transform, important function of the mathematical modeling in scientific technological advance increasingly by
To the most attention of mathematical region and engineering circles, it have become modern science and technology worker's indispensability significant capability itOne。
In order to which the needs and culture high quality, high-level skilled personnel, mathematical modeling that adapt to scientific technological advance exist
Gradually carry out in university education, more and more university are carrying out the teaching of A Course of Mathematical Modelling and participating in open both at home and abroad
Mathematical modeling contest, Modeling Teaching of Mathematics and contest as the reform in education of institution of higher learning and are cultivated into high-level scientific and technological people
Mathematical modeling is combined by one importance of, present many universities and colleges with the reform in education, makes great efforts to explore more effective
Modeling Teaching of Mathematics method and the new approaches for cultivating the talent geared to the 21st century, compared with other Mathematics courses of China university,
Mathematical modeling has the features such as difficulty is big, involves a wide range of knowledge, flexible form, high to Faculty and Students' requirement, the teaching of mathematical modeling
Itself be one constantly explore, constantly bring forth new ideas, the process of constantly improve and raising.
Whether any class practical problem mathematically is solved in science and technology and production field, or is combined with other subject
Cross discipline is formed, primary and key a step is to establish the mathematical model of research object, and calculated solution.Mathematics is built
The effect of mould and computer technology in the era of knowledge-driven economy is further strengthened.
When being modeled using computer technology, needs to be related to largely calculating and professional knowledge, operates and its cumbersome,
It is difficult to grasp, certain difficulty is brought with merging for mathematical modeling to computer.
Invention content
The purpose of the present invention is against the above deficiency, it is proposed that is calculated when a kind of reduction computer modeling and professional knowledge
It calculates, improves the Mathematical Modeling Methods using computer hyperspace of operation ease and Grasping level.
The present invention specifically adopts the following technical scheme that：
A kind of Mathematical Modeling Methods using computer hyperspace include the following steps：
Step 1：By computer acquisition system gathered data and analyze discrete, computer acquisition system includes hardware list
Member and software unit, after computer acquisition system determines that sampling period, sampling period determine according to sampling thheorem and system index
The function distribution for carrying out the hardware and software of computer acquisition system, determines the allocation plan of computer acquisition system；
Step 2：Model hypothesis is carried out according to discrete data, space dimensionality is determined, distinguishes each dimension data of hyperspace
Insert determinant；The corresponding matrix of hypothesized model is A, first finds out the characteristic value of matrix A, corresponds to each characteristic value solving equations
| λ E-A |=0, each solution of equations is a characteristic vector space of character pair value, and the dimension of solution is hyperspace
Dimension, the base of solution is that the base row of hyperspace arranges；
Step 3：Determinant is simplified by linear algebra theory, and establishes functional relation；
Step 4：Discrete data in step 1 is brought into and carries out verification operation in function；
Step 5：If the error verified in step 4 is excessive, return to step four re-establishes functional relation；
Step 6：Reach stipulated number if retried, return to step two redefines suitable space dimensionality；
Step 7：Simplify the mathematical relationship between each dimension, each dimension is made individually to linearize.
Preferably, the computer acquisition system is using microprocessor chip, single-chip microprocessor chip, single board computer, standard
Functional template or personal microcomputer are as control process machine.
Preferably, the operation interface of the computer acquisition system includes：Input and modification source program unit show and beat
Print various parameters unit, the selecting unit of working method, the running unit of startup and halt system.
Preferably, the hardware cell in the step 1 is centered on computer, including peripheral circuit part.
Preferably, the software unit in the step 1 includes several program modules：Initialization program module, self-test journey
Sequence module, capture program module, data processor module, printing and display program module, printing alert program module and tune
Die trial block, wherein low previous module is repeated to call by high previous module.
Preferably, the debugging module subroutine is debugged, and constantly changes the mistake of appearance, until program debugging
It finishes, then main program is connected into a complete program with subprogram and is debugged, when debugging routine, it is disconnected to insert people in a program
Point, partition running, piecewise debug, finally, by the program Solidification debugged to EPRO or deposit disk.
Preferably, in the step 3, the method that determinant simplifies includes definition method, triangle method, even addition, depression of order
Method, recurrence method, edged method, mathematical induction and laplace expansion.
The present invention has the advantages that：This method is simple, and hyperspace is digitized and linearized, is provided
Perfect modeling procedure, need not be related to largely calculating and professional knowledge, operation and its simple.
Description of the drawings
Fig. 1 is the Mathematical Modeling Methods flow chart using computer hyperspace.
Specific implementation mode
The specific implementation mode of the present invention is described further in the following with reference to the drawings and specific embodiments：
As shown in Figure 1, step 1：By computer acquisition system gathered data and carry out analyzing discrete, computer acquisition system
Including hardware cell and software unit, computer acquisition system determines the sampling period according to sampling thheorem and system index, sampling
The function distribution of the hardware and software of progress computer acquisition system, determines the configuration side of computer acquisition system after period determines
Case；
Step 2：Model hypothesis is carried out according to discrete data, space dimensionality is determined, distinguishes each dimension data of hyperspace
Insert determinant；The corresponding matrix of hypothesized model is A, first finds out the characteristic value of matrix A, corresponds to each characteristic value solving equations
| λ E-A |=0, each solution of equations is a characteristic vector space of character pair value, and the dimension of solution is hyperspace
Dimension, the base of solution is that the base row of hyperspace arranges；
Step 3：Determinant is simplified by linear algebra theory, and establishes functional relation；
Step 4：Discrete data in step 1 is brought into and carries out verification operation in function；
Step 5：If the error verified in step 4 is excessive, return to step four re-establishes functional relation；
Step 6：Reach regulation if retried（It is 5 times default）Number, then return to step two, redefine suitable space dimensionality；
Step 7：Simplify the mathematical relationship between each dimension, each dimension is made individually to linearize.
Computer acquisition system using microprocessor chip, single-chip microprocessor chip, single board computer, standard feature template or
Personal microcomputer is as control process machine.
The operation interface of computer acquisition system includes：Input and modification source program unit, display and printing various parameters
Unit, the selecting unit of working method, the running unit of startup and halt system.
Hardware cell in step 1 is centered on computer, including peripheral circuit part.
Software unit in step 1 includes several program modules：Initialization program module, self-check program module, acquisition
Program module, data processor module, printing and display program module, printing alert program module and debugging module, wherein
Low previous module is repeated to call by high previous module.
Debugging module subroutine is debugged, and the mistake of appearance is constantly changed, until program debugging finishes, then will be led
Program connects into a complete program with subprogram and is debugged, and when debugging routine, inserts people's breakpoint, segmentation fortune in a program
Row, piecewise debug, finally, by the program Solidification debugged to EPRO or deposit disk.
In step 3, determinant simplify method include definition method, triangle method, even addition, the depression of order, recurrence method,
Edged method, mathematical induction and laplace expansion.
Wherein, triangle method：Determinant always is turned to upper triangle or lower triangle by the property of determinant,
This method is suitable for low order determinant
The form of upper triangular determinant is as follows：
Lower triangular determinant is same as above triangular determinant.
Edged method：
N rank determinants are increased the row of a line one and become n+1 rank determinants, then are calculated as a result, some ranks by property abbreviation
Formula needs liter rank twice.
The maximum feature for rising rank method seeks to look for every row or the identical factor of each column, after rising rank, so that it may to utilize ranks
Most elements are turned to 0 by the property of formula, thus achieve the effect that simplify calculating, wherein add the mode one of row and column
As there are five types of：First trip first, first trip terminal column, footline first, the position of footline terminal column and general ranks.
Certainly, above description is not limitation of the present invention, and the present invention is also not limited to the example above, this technology neck
The variations, modifications, additions or substitutions that the technical staff in domain is made in the essential scope of the present invention should also belong to the present invention's
Protection domain.
Claims (7)
1. a kind of Mathematical Modeling Methods using computer hyperspace, which is characterized in that include the following steps：
Step 1：By computer acquisition system gathered data and analyze discrete, computer acquisition system includes hardware list
Member and software unit, after computer acquisition system determines that sampling period, sampling period determine according to sampling thheorem and system index
The function distribution for carrying out the hardware and software of computer acquisition system, determines the allocation plan of computer acquisition system；
Step 2：Model hypothesis is carried out according to discrete data, space dimensionality is determined, distinguishes each dimension data of hyperspace
Insert determinant；The corresponding matrix of hypothesized model is A, first finds out the characteristic value of matrix A, corresponds to each characteristic value solving equations
| λ E-A |=0, each solution of equations is a characteristic vector space of character pair value, and the dimension of solution is hyperspace
Dimension, the base of solution is that the base row of hyperspace arranges；
Step 3：Determinant is simplified by linear algebra theory, and establishes functional relation；
Step 4：Discrete data in step 1 is brought into and carries out verification operation in function；
Step 5：If the error verified in step 5 is excessive, return to step four re-establishes functional relation；
Step 6：Reach stipulated number if retried, return to step two redefines suitable space dimensionality；
Step 7：Simplify the mathematical relationship between each dimension, each dimension is made individually to linearize.
2. a kind of Mathematical Modeling Methods using computer hyperspace as described in claim 1, which is characterized in that the meter
Calculation machine acquisition system is using microprocessor chip, single-chip microprocessor chip, single board computer, standard feature template or personal microcomputer
Calculation machine is as control process machine.
3. a kind of Mathematical Modeling Methods using computer hyperspace as described in claim 1, which is characterized in that the meter
The operation interface of calculation machine acquisition system includes：Input and modification source program unit, display and printing various parameters unit, work side
The selecting unit of formula, the running unit of startup and halt system.
4. a kind of Mathematical Modeling Methods using computer hyperspace as described in claim 1, which is characterized in that the step
Hardware cell in rapid one is centered on computer, including peripheral circuit part.
5. a kind of Mathematical Modeling Methods using computer hyperspace as described in claim 1, which is characterized in that the step
Software unit in rapid one includes several program modules：Initialization program module, self-check program module, capture program module,
Data processor module, printing and display program module, printing alert program module and debugging module, wherein low previous module
It is repeated to call by high previous module.
6. a kind of Mathematical Modeling Methods using computer hyperspace as claimed in claim 5, which is characterized in that the tune
Die trial block subroutine is debugged, and the mistake of appearance is constantly changed, until program debugging finishes, then by main program and sub- journey
Sequence connects into a complete program and is debugged, and when debugging routine, inserts people's breakpoint in a program, partition running excludes paragraph by paragraph
Mistake, finally, by the program Solidification debugged to EPRO or deposit disk.
7. a kind of Mathematical Modeling Methods using computer hyperspace as described in claim 1, which is characterized in that the step
In rapid three, the method that determinant simplifies includes definition method, triangle method, even addition, the depression of order, recurrence method, edged method, mathematics
Induction and laplace expansion.
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Cited By (2)
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| CN109657189A (en) * | 2018-12-20 | 2019-04-19 | 南阳理工学院 | A kind of Mathematical Modeling Methods using computer hyperspace |
| CN111090905A (en) * | 2019-12-23 | 2020-05-01 | 陕西理工大学 | Mathematical modeling method using computer multidimensional space |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111090905A (en) * | 2019-12-23 | 2020-05-01 | 陕西理工大学 | Mathematical modeling method using computer multidimensional space |
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Application publication date: 20180921 |