Successive Approximations: A Step-by-Step Approach to Refining Solutions

Successive Approximations: A Step-by-Step Approach to Solutions

Successive Approximations: A Step-by-Step Approach to Solutions

Kaizen or Successive approximations, also known as iterative methods, are a powerful technique used to find solutions to equations or problems that might be difficult or impossible to solve directly. 

The core idea is to start with an initial guess and then refine that guess through a series of steps, gradually getting closer and closer to the actual solution and desired outcome.

How it Works

 • Initial Guess: Begin with an educated guess for the solution. This initial guess can be based on intuition, prior knowledge, or even a random starting point.

• Iteration: Apply a specific algorithm or formula to the initial guess to obtain a new, hopefully improved, approximation.

• Repeat: Use the new approximation as the input for the next iteration. This process is repeated iteratively, with each step producing a closer approximation to the true solution.

• Convergence: Ideally, the sequence of approximations will converge, meaning that the difference between successive approximations becomes smaller and smaller as the iterations proceed. When the difference becomes sufficiently small, the process can be stopped, and the final approximation is accepted as the solution.

Applications of Successive Approximations

Successive approximations find applications in various fields, including:

 • Mathematics

• Engineering

• Computer Science

• Psychology

• Organizational Behavior

• Manufacturing

• Service Industries

Advantages of Successive Approximations

 • Handle Complex Problems.

 • Versatility: Applicable to a wide range of problems in various fields.

 • Flexibility: Can be adapted to specific problem characteristics and computational constraints.

In Conclusion:

Successive approximations is a valuable tool for tackling challenging problems.

Kenneth H. Little, MA

New Hampshire

Trust & Faith

Parenting requires two key elements: trust and faith. It's very important that parents
trust their children and have faith in their innate goodness and capacity, while
continuously working to develop the required skills, ability, and character.
With constructive proactive parenting the likelihood is very high that your children
will turn out to be the good, capable, successful adults they were born to be. 

Believe this. Believe in your child’s natural goodness and innate ability from birth on.

The probability of a good outcome declines as parents implement parenting plans and
methods that are based in fear, anxiety, anger, and mistrust. For example, if you
believe that children are inherently sneaky and dishonest, you are likely to parent
them in a way that increases their sneakiness and dishonesty. Similarly, overly
restrictive parenting designed to increase child obedience and safety often inspires
increased rebellion and risky behaviors.

Trust

I often hear parents say to a child who has made a mistake -- "you broke my trust".
This in my view is a deep parental mistake, more akin to shaming than guiding and
correcting. Under what circumstances does a parent think create illusory conditions
of trust based on the expectation that their child will never make a mistake?

Mistakes are expected, not surprises. Trust your children to make mistakes as they
grow up. 

Children are born with natural goodness and abilities, not as perfect beings. Life is a rigorous and demanding practice-to-mastery activity. Mistakes are an expected part of life. When a child makes a mistake, it will be more reasonable and honest for a parent to say, "ah, that was expected. Let's see if we can figure out what went wrong." Mistakes are an expected part of growing up, not betrayals of trust. It's much more reasonable and accurate to trust that children will make mistakes, understanding that this is a very ordinary part of growing up.

Smile at the mistakes and reassure them.

Faith

Have faith in your children. Believe in them, that they are essentially good and
capable. Children make mistakes. They will need coaching and corrective guidance
on life skills, but this does not make them bad. "Bad" behaviors are much more
accurately seen as expected mistakes.

This is not an exercise in semantics.

How you feel about children in general will leak out all over your children. Many
parents (and teachers) that I've worked with over the years have expressed the belief
that children are essentially "bad", that they are liars and are always "up to no good",
trying to get away with some bad behavior. This is a belief, a basic assumption about
children and human beings. It's not a fact. 

While it may apply to a very few, most children are not inherently "bad". If you believe that children are basically bad, this belief will be infused into every parent-child interaction: it will be in your eyes, in your tone of voice, in the conclusions you jump to, and in the way you talk with your child after events. Your child will gradually internalize your beliefs over time and have increasingly bad behavior as a result.

This parenting approach is a self-fulfilling prophecy. 

The parent believes it and interacts with their children accordingly who then internalize the belief and ... act it out in the real world.

My strongest possible recommendation is for you to question your beliefs about
children and work continuously to develop a belief in their inherent ability and
goodness. They do not misbehave intentionally as an expression of "being bad"
humans. Children are inherently "good'. Think of misbehavior events as “just a mistake”, not a catastrophic indicator that they will grow up to be felons or failures.

Note: there are a very few children who do certain things that are indicators of a much
larger problem. This is rare. I have worked with these children. They do need extra
help. It's unlikely that your child is this child. I'll do a post on red flags another time,
but just as an example, cruelty toward animals is an example of a child in significant
distress. If you are concerned, consult with your child's medical doctor first. If you
are still concerned speak with a clinical specialist.

Even if your child is in a high-risk category, your belief in their essential goodness
and ability to overcome can have a significant constructive impact on future outcomes
while in the opposite direction, your belief that they are inherently bad is more likely
to cement their destructive future fate.

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Kenneth H. Little, MA / 135 Lee Brook Road / Thornton, NH 03285 / 603-726-1006 / Achieve-ES.com

© 2019 Kenneth H. Little. All rights reserved. 

Successive Approximations ... Toward Success

A brief talk with a colleague this morning prompted me to write this short essay. She was describing to me how frustrating it is to walk out into the living room and realize how much mess has accumulated while your children sit and giggle watching youtube videos, apparently oblivious to the carnage surrounding them.

I know this feeling.  It can be infuriating. The urge to scream can be powerful.


But First, Ask ... is this an emergency?

Take a step back.  Evaluate.  Is this an emergency?  Is anyone gushing blood or on fire?  If yes, it's an emergency -- stay calm, think clearly, take action.  If no one is gushing blood or on fire, there is no emergency -- stay calm, think clearly, delay taking action.  Emergency or not, stay calm - think with a clear head.

Own the Problem

First, always own the problem.  If the family is not functioning as desired, responsibility falls to the leadership. The family leaders are responsible for creating the necessary systems and structures and for providing the support and training needed to facilitate the desired outcome.  Consider for a moment, if your knee-jerk reaction is to blame the children ... you are committing a fundamental attribution error.  Your children have always existed within your family culture.   

1. Take a step back.  Clear your head.
2. Consider the problem carefully, where is the breakdown?
3. Consider potential solutions - what needs to be changed or re-organized?
4. Convene a family meeting, include all stake holders.
5. Explain the problem and your vision of the desired outcome. 
6. Invite members to problem solve - on how to get from the current situation to the desired outcome. 
7. Brainstorm, Try-storm, Generate a list of potential solutions. 
8. Evaluate potential solutions for goodness of fit. 
9. Pick the best.  Agreeable to all.
10. Agree to implement on a trial basis. 
11. After a short trial period, evaluate outcome. 
12. If the problem is solved, carry on. 
13. If the problem is not solved, return to step 1.

Successive Approximations

Understand this term.  Successive approximation describes a process of gradually refining outcomes to come closer and closer to the envisioned standard.  At first family members may not be skilled in accomplishing the tasks as required.  For example, vacuuming may be disorganized, the dish washer may be loaded incorrectly, etc.  All tasks and activities start out sloppy and improve with practice and training over time.

In the illustration above, step 4 represents the desired outcome.  It's fairly tight, precise, on target.  Step 1 represents the not very precise first approximation.  With training and practice outcomes improve through the steps. The 4 steps illustrated above is more symbolic than actual.  When it comes to raising children, the are many, many more steps in achieving success.

Set-backs and Regressions

It's important to expect set-backs and regressions.  The process of improvement looks more like a stock market graph that a straight line.   The are periods of growth followed by regressions and set-back as each family member navigates various struggles and challenges, and experiences of success. During easier times, expect performance improvement.  During tough times, expect regression, performance decline. Teach and practice regrouping skills, the ability to bounce back from adversity. 

Be Supportive

Encourage and re-assure. Practice leads to mastery. Failure is not a disaster, but an opportunity to be supportive, evaluate what went wrong, and to make improvements over time. Failures are opportunities to practice regrouping skills.